{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0001","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(-2)x²+(-12)x+(-3)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=-2。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034001,"parameters":{"a":-2,"b":-12,"c":-3,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":-2,\"b\":-12,\"c\":-3,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0002","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(-1)x²+(-11)x+(-2)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=-1。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034002,"parameters":{"a":-1,"b":-11,"c":-2,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":-1,\"b\":-11,\"c\":-2,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0003","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(0)x²+(-10)x+(-1)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"否","explanation_zh":"a=0。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034003,"parameters":{"a":0,"b":-10,"c":-1,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":0,\"b\":-10,\"c\":-1,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0004","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(1)x²+(-9)x+(0)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=1。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034004,"parameters":{"a":1,"b":-9,"c":0,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":1,\"b\":-9,\"c\":0,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0005","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(2)x²+(-8)x+(1)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=2。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034005,"parameters":{"a":2,"b":-8,"c":1,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":2,\"b\":-8,\"c\":1,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0006","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(-2)x²+(-7)x+(2)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=-2。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034006,"parameters":{"a":-2,"b":-7,"c":2,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":-2,\"b\":-7,\"c\":2,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0007","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(-1)x²+(-6)x+(3)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=-1。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034007,"parameters":{"a":-1,"b":-6,"c":3,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":-1,\"b\":-6,\"c\":3,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0008","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(0)x²+(-5)x+(-3)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"否","explanation_zh":"a=0。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034008,"parameters":{"a":0,"b":-5,"c":-3,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":0,\"b\":-5,\"c\":-3,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0009","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(1)x²+(-4)x+(-2)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=1。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034009,"parameters":{"a":1,"b":-4,"c":-2,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":1,\"b\":-4,\"c\":-2,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0010","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(2)x²+(-3)x+(-1)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=2。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034010,"parameters":{"a":2,"b":-3,"c":-1,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":2,\"b\":-3,\"c\":-1,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0011","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(-2)x²+(-2)x+(0)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=-2。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034011,"parameters":{"a":-2,"b":-2,"c":0,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":-2,\"b\":-2,\"c\":0,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0012","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(-1)x²+(-1)x+(1)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=-1。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034012,"parameters":{"a":-1,"b":-1,"c":1,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":-1,\"b\":-1,\"c\":1,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0013","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(0)x²+(0)x+(2)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"否","explanation_zh":"a=0。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034013,"parameters":{"a":0,"b":0,"c":2,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":0,\"b\":0,\"c\":2,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0014","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(1)x²+(1)x+(3)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=1。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034014,"parameters":{"a":1,"b":1,"c":3,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":1,\"b\":1,\"c\":3,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0015","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(2)x²+(2)x+(-3)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=2。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034015,"parameters":{"a":2,"b":2,"c":-3,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":2,\"b\":2,\"c\":-3,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0016","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(-2)x²+(3)x+(-2)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=-2。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034016,"parameters":{"a":-2,"b":3,"c":-2,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":-2,\"b\":3,\"c\":-2,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0017","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(-1)x²+(4)x+(-1)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=-1。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034017,"parameters":{"a":-1,"b":4,"c":-1,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":-1,\"b\":4,\"c\":-1,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0018","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(0)x²+(5)x+(0)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"否","explanation_zh":"a=0。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034018,"parameters":{"a":0,"b":5,"c":0,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":0,\"b\":5,\"c\":0,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0019","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(1)x²+(6)x+(1)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=1。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034019,"parameters":{"a":1,"b":6,"c":1,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":1,\"b\":6,\"c\":1,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0020","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(2)x²+(7)x+(2)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=2。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034020,"parameters":{"a":2,"b":7,"c":2,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":2,\"b\":7,\"c\":2,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0021","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(-2)x²+(8)x+(3)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=-2。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034021,"parameters":{"a":-2,"b":8,"c":3,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":-2,\"b\":8,\"c\":3,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0022","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(-1)x²+(9)x+(-3)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=-1。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034022,"parameters":{"a":-1,"b":9,"c":-3,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":-1,\"b\":9,\"c\":-3,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0023","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(0)x²+(10)x+(-2)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"否","explanation_zh":"a=0。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034023,"parameters":{"a":0,"b":10,"c":-2,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":0,\"b\":10,\"c\":-2,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0024","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(1)x²+(11)x+(-1)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=1。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034024,"parameters":{"a":1,"b":11,"c":-1,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":1,\"b\":11,\"c\":-1,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0025","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式形式合法性","stem_zh":"在實數論域，(2)x²+(12)x+(0)=0 是否為一元二次方程式？","answer":{"kind":"short_text","value":"是","explanation_zh":"a=2。二次係數必須非零；a=0 的式子即使寫出 x²，也不屬於二次方程式。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式形式合法性"]},"variant":{"family_id":"qf-quadratic-form-validity","seed":202610034025,"parameters":{"a":2,"b":12,"c":0,"domain":"reals","operation":"quadratic_form","semantic_template":"qf-quadratic-form-validity/{\"a\":2,\"b\":12,\"c\":0,\"domain\":\"reals\",\"operation\":\"quadratic_form\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0026","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(0)x+(1)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=-4；相異實根數=0","explanation_zh":"D=-4；相異實根數=0。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034026,"parameters":{"a":1,"b":0,"c":1,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":0,\"c\":1,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0027","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(0)x+(0)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=0；相異實根數=1","explanation_zh":"D=0；相異實根數=1。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034027,"parameters":{"a":1,"b":0,"c":0,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":0,\"c\":0,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0028","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(-1)x²+(0)x+(1)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=4；相異實根數=2","explanation_zh":"D=4；相異實根數=2。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034028,"parameters":{"a":-1,"b":0,"c":1,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":-1,\"b\":0,\"c\":1,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0029","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(2)x+(2)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=-4；相異實根數=0","explanation_zh":"D=-4；相異實根數=0。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034029,"parameters":{"a":1,"b":2,"c":2,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":2,\"c\":2,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0030","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(2)x+(1)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=0；相異實根數=1","explanation_zh":"D=0；相異實根數=1。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034030,"parameters":{"a":1,"b":2,"c":1,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":2,\"c\":1,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0031","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(-1)x²+(1)x+(2)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=9；相異實根數=2","explanation_zh":"D=9；相異實根數=2。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034031,"parameters":{"a":-1,"b":1,"c":2,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":-1,\"b\":1,\"c\":2,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0032","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(4)x+(5)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=-4；相異實根數=0","explanation_zh":"D=-4；相異實根數=0。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034032,"parameters":{"a":1,"b":4,"c":5,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":4,\"c\":5,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0033","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(4)x+(4)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=0；相異實根數=1","explanation_zh":"D=0；相異實根數=1。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034033,"parameters":{"a":1,"b":4,"c":4,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":4,\"c\":4,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0034","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(-1)x²+(2)x+(3)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=16；相異實根數=2","explanation_zh":"D=16；相異實根數=2。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034034,"parameters":{"a":-1,"b":2,"c":3,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":-1,\"b\":2,\"c\":3,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0035","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(6)x+(10)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=-4；相異實根數=0","explanation_zh":"D=-4；相異實根數=0。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034035,"parameters":{"a":1,"b":6,"c":10,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":6,\"c\":10,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0036","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(6)x+(9)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=0；相異實根數=1","explanation_zh":"D=0；相異實根數=1。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034036,"parameters":{"a":1,"b":6,"c":9,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":6,\"c\":9,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0037","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(-1)x²+(3)x+(4)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=25；相異實根數=2","explanation_zh":"D=25；相異實根數=2。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034037,"parameters":{"a":-1,"b":3,"c":4,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":-1,\"b\":3,\"c\":4,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0038","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(8)x+(17)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=-4；相異實根數=0","explanation_zh":"D=-4；相異實根數=0。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034038,"parameters":{"a":1,"b":8,"c":17,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":8,\"c\":17,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0039","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(8)x+(16)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=0；相異實根數=1","explanation_zh":"D=0；相異實根數=1。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034039,"parameters":{"a":1,"b":8,"c":16,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":8,\"c\":16,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0040","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(-1)x²+(4)x+(5)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=36；相異實根數=2","explanation_zh":"D=36；相異實根數=2。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034040,"parameters":{"a":-1,"b":4,"c":5,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":-1,\"b\":4,\"c\":5,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0041","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(10)x+(26)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=-4；相異實根數=0","explanation_zh":"D=-4；相異實根數=0。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034041,"parameters":{"a":1,"b":10,"c":26,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":10,\"c\":26,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0042","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(10)x+(25)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=0；相異實根數=1","explanation_zh":"D=0；相異實根數=1。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034042,"parameters":{"a":1,"b":10,"c":25,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":10,\"c\":25,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0043","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(-1)x²+(5)x+(6)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=49；相異實根數=2","explanation_zh":"D=49；相異實根數=2。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034043,"parameters":{"a":-1,"b":5,"c":6,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":-1,\"b\":5,\"c\":6,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0044","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(12)x+(37)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=-4；相異實根數=0","explanation_zh":"D=-4；相異實根數=0。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034044,"parameters":{"a":1,"b":12,"c":37,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":12,\"c\":37,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0045","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(12)x+(36)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=0；相異實根數=1","explanation_zh":"D=0；相異實根數=1。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034045,"parameters":{"a":1,"b":12,"c":36,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":12,\"c\":36,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0046","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(-1)x²+(6)x+(7)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=64；相異實根數=2","explanation_zh":"D=64；相異實根數=2。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034046,"parameters":{"a":-1,"b":6,"c":7,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":-1,\"b\":6,\"c\":7,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0047","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(14)x+(50)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=-4；相異實根數=0","explanation_zh":"D=-4；相異實根數=0。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034047,"parameters":{"a":1,"b":14,"c":50,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":14,\"c\":50,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0048","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(14)x+(49)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=0；相異實根數=1","explanation_zh":"D=0；相異實根數=1。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034048,"parameters":{"a":1,"b":14,"c":49,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":14,\"c\":49,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0049","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(-1)x²+(7)x+(8)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=81；相異實根數=2","explanation_zh":"D=81；相異實根數=2。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034049,"parameters":{"a":-1,"b":7,"c":8,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":-1,\"b\":7,\"c\":8,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0050","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"判別式與相異實根數","stem_zh":"在實數論域，(1)x²+(16)x+(65)=0 的 a≠0。求判別式 D 及相異實根數。","answer":{"kind":"short_text","value":"D=-4；相異實根數=0","explanation_zh":"D=-4；相異實根數=0。D=b²−4ac；負、零、正分別給零、一、兩個相異實根，不把重根算兩次。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["判別式與相異實根數"]},"variant":{"family_id":"qf-quadratic-discriminant","seed":202610034050,"parameters":{"a":1,"b":16,"c":65,"domain":"reals","operation":"discriminant","semantic_template":"qf-quadratic-discriminant/{\"a\":1,\"b\":16,\"c\":65,\"domain\":\"reals\",\"operation\":\"discriminant\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0051","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(2)x²+(16)x+(24)=0 的 a≠0。最簡正分母候選 x=-6/1 是否為解？","answer":{"kind":"short_text","value":"是","explanation_zh":"分母清除後=0。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是是。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034051,"parameters":{"a":2,"b":16,"c":24,"p":-6,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":2,\"b\":16,\"c\":24,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"-6\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0052","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(-4)x²+(-26)x+(-22)=0 的 a≠0。最簡正分母候選 x=-5/1 是否為解？","answer":{"kind":"short_text","value":"否","explanation_zh":"分母清除後=8。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是否。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034052,"parameters":{"a":-4,"b":-26,"c":-22,"p":-5,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":-4,\"b\":-26,\"c\":-22,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"-5\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0053","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(6)x²+(30)x+(0)=0 的 a≠0。最簡正分母候選 x=-5/1 是否為解？","answer":{"kind":"short_text","value":"是","explanation_zh":"分母清除後=0。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是是。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034053,"parameters":{"a":6,"b":30,"c":0,"p":-5,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":6,\"b\":30,\"c\":0,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"-5\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0054","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(-2)x²+(-7)x+(9)=0 的 a≠0。最簡正分母候選 x=-4/1 是否為解？","answer":{"kind":"short_text","value":"否","explanation_zh":"分母清除後=5。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是否。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034054,"parameters":{"a":-2,"b":-7,"c":9,"p":-4,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":-2,\"b\":-7,\"c\":9,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"-4\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0055","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(4)x²+(8)x+(-32)=0 的 a≠0。最簡正分母候選 x=-4/1 是否為解？","answer":{"kind":"short_text","value":"是","explanation_zh":"分母清除後=0。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是是。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034055,"parameters":{"a":4,"b":8,"c":-32,"p":-4,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":4,\"b\":8,\"c\":-32,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"-4\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0056","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(-6)x²+(-33)x+(-42)=0 的 a≠0。最簡正分母候選 x=-3/1 是否為解？","answer":{"kind":"short_text","value":"否","explanation_zh":"分母清除後=3。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是否。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034056,"parameters":{"a":-6,"b":-33,"c":-42,"p":-3,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":-6,\"b\":-33,\"c\":-42,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"-3\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0057","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(2)x²+(8)x+(6)=0 的 a≠0。最簡正分母候選 x=-3/1 是否為解？","answer":{"kind":"short_text","value":"是","explanation_zh":"分母清除後=0。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是是。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034057,"parameters":{"a":2,"b":8,"c":6,"p":-3,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":2,\"b\":8,\"c\":6,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"-3\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0058","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(-4)x²+(-10)x+(0)=0 的 a≠0。最簡正分母候選 x=-2/1 是否為解？","answer":{"kind":"short_text","value":"否","explanation_zh":"分母清除後=4。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是否。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034058,"parameters":{"a":-4,"b":-10,"c":0,"p":-2,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":-4,\"b\":-10,\"c\":0,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"-2\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0059","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(6)x²+(6)x+(-12)=0 的 a≠0。最簡正分母候選 x=-2/1 是否為解？","answer":{"kind":"short_text","value":"是","explanation_zh":"分母清除後=0。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是是。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034059,"parameters":{"a":6,"b":6,"c":-12,"p":-2,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":6,\"b\":6,\"c\":-12,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"-2\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0060","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(-2)x²+(1)x+(6)=0 的 a≠0。最簡正分母候選 x=-1/1 是否為解？","answer":{"kind":"short_text","value":"否","explanation_zh":"分母清除後=3。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是否。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034060,"parameters":{"a":-2,"b":1,"c":6,"p":-1,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":-2,\"b\":1,\"c\":6,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"-1\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0061","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(4)x²+(12)x+(8)=0 的 a≠0。最簡正分母候選 x=-1/1 是否為解？","answer":{"kind":"short_text","value":"是","explanation_zh":"分母清除後=0。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是是。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034061,"parameters":{"a":4,"b":12,"c":8,"p":-1,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":4,\"b\":12,\"c\":8,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"-1\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0062","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(-6)x²+(-9)x+(-3)=0 的 a≠0。最簡正分母候選 x=0/1 是否為解？","answer":{"kind":"short_text","value":"否","explanation_zh":"分母清除後=-3。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是否。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034062,"parameters":{"a":-6,"b":-9,"c":-3,"p":0,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":-6,\"b\":-9,\"c\":-3,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"0\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0063","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(2)x²+(0)x+(0)=0 的 a≠0。最簡正分母候選 x=0/1 是否為解？","answer":{"kind":"short_text","value":"是","explanation_zh":"分母清除後=0。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是是。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034063,"parameters":{"a":2,"b":0,"c":0,"p":0,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":2,\"b\":0,\"c\":0,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"0\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0064","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(-4)x²+(6)x+(-2)=0 的 a≠0。最簡正分母候選 x=1/1 是否為解？","answer":{"kind":"short_text","value":"是","explanation_zh":"分母清除後=0。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是是。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034064,"parameters":{"a":-4,"b":6,"c":-2,"p":1,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":-4,\"b\":6,\"c\":-2,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"1\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0065","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(6)x²+(-18)x+(12)=0 的 a≠0。最簡正分母候選 x=1/1 是否為解？","answer":{"kind":"short_text","value":"是","explanation_zh":"分母清除後=0。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是是。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034065,"parameters":{"a":6,"b":-18,"c":12,"p":1,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":6,\"b\":-18,\"c\":12,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"1\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0066","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(-2)x²+(-1)x+(6)=0 的 a≠0。最簡正分母候選 x=2/1 是否為解？","answer":{"kind":"short_text","value":"否","explanation_zh":"分母清除後=-4。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是否。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034066,"parameters":{"a":-2,"b":-1,"c":6,"p":2,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":-2,\"b\":-1,\"c\":6,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"2\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0067","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(4)x²+(-4)x+(-8)=0 的 a≠0。最簡正分母候選 x=2/1 是否為解？","answer":{"kind":"short_text","value":"是","explanation_zh":"分母清除後=0。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是是。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034067,"parameters":{"a":4,"b":-4,"c":-8,"p":2,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":4,\"b\":-4,\"c\":-8,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"2\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0068","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(-6)x²+(15)x+(0)=0 的 a≠0。最簡正分母候選 x=3/1 是否為解？","answer":{"kind":"short_text","value":"否","explanation_zh":"分母清除後=-9。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是否。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034068,"parameters":{"a":-6,"b":15,"c":0,"p":3,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":-6,\"b\":15,\"c\":0,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"3\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0069","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(2)x²+(-8)x+(6)=0 的 a≠0。最簡正分母候選 x=3/1 是否為解？","answer":{"kind":"short_text","value":"是","explanation_zh":"分母清除後=0。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是是。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034069,"parameters":{"a":2,"b":-8,"c":6,"p":3,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":2,\"b\":-8,\"c\":6,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"3\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0070","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(-4)x²+(22)x+(-28)=0 的 a≠0。最簡正分母候選 x=4/1 是否為解？","answer":{"kind":"short_text","value":"否","explanation_zh":"分母清除後=-4。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是否。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034070,"parameters":{"a":-4,"b":22,"c":-28,"p":4,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":-4,\"b\":22,\"c\":-28,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"4\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0071","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(6)x²+(-12)x+(-48)=0 的 a≠0。最簡正分母候選 x=4/1 是否為解？","answer":{"kind":"short_text","value":"是","explanation_zh":"分母清除後=0。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是是。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034071,"parameters":{"a":6,"b":-12,"c":-48,"p":4,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":6,\"b\":-12,\"c\":-48,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"4\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0072","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(-2)x²+(7)x+(9)=0 的 a≠0。最簡正分母候選 x=5/1 是否為解？","answer":{"kind":"short_text","value":"否","explanation_zh":"分母清除後=-6。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是否。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034072,"parameters":{"a":-2,"b":7,"c":9,"p":5,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":-2,\"b\":7,\"c\":9,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"5\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0073","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(4)x²+(-20)x+(0)=0 的 a≠0。最簡正分母候選 x=5/1 是否為解？","answer":{"kind":"short_text","value":"是","explanation_zh":"分母清除後=0。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是是。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034073,"parameters":{"a":4,"b":-20,"c":0,"p":5,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":4,\"b\":-20,\"c\":0,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"5\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0074","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(-6)x²+(39)x+(-33)=0 的 a≠0。最簡正分母候選 x=6/1 是否為解？","answer":{"kind":"short_text","value":"否","explanation_zh":"分母清除後=-15。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是否。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034074,"parameters":{"a":-6,"b":39,"c":-33,"p":6,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":-6,\"b\":39,\"c\":-33,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"6\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0075","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"精確有理根代入驗證","stem_zh":"在實數論域，(2)x²+(-16)x+(24)=0 的 a≠0。最簡正分母候選 x=6/1 是否為解？","answer":{"kind":"short_text","value":"是","explanation_zh":"分母清除後=0。因 q=1>0，把代入式乘 q² 後判斷是否等於零，答案是是。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["精確有理根代入驗證"]},"variant":{"family_id":"qf-quadratic-root-verification","seed":202610034075,"parameters":{"a":2,"b":-16,"c":24,"p":6,"q":1,"domain":"reals","operation":"root_verification","semantic_template":"qf-quadratic-root-verification/{\"a\":2,\"b\":-16,\"c\":24,\"domain\":\"reals\",\"operation\":\"root_verification\",\"p\":\"6\",\"q\":\"1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0076","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(1)x²+(0)x+(0)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{0/1}","explanation_zh":"D=0；根={0/1}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034076,"parameters":{"a":1,"b":0,"c":0,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":1,\"b\":0,\"c\":0,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0077","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(-1)x²+(2)x+(-1)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{1/1}","explanation_zh":"D=0；根={1/1}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034077,"parameters":{"a":-1,"b":2,"c":-1,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":-1,\"b\":2,\"c\":-1,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0078","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(6)x²+(32)x+(10)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-5/1, -1/3}","explanation_zh":"D=784；根={-5/1, -1/3}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034078,"parameters":{"a":6,"b":32,"c":10,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":6,\"b\":32,\"c\":10,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0079","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(-6)x²+(-27)x+(0)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-9/2, 0/1}","explanation_zh":"D=729；根={-9/2, 0/1}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034079,"parameters":{"a":-6,"b":-27,"c":0,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":-6,\"b\":-27,\"c\":0,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0080","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(6)x²+(22)x+(-8)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-4/1, 1/3}","explanation_zh":"D=676；根={-4/1, 1/3}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034080,"parameters":{"a":6,"b":22,"c":-8,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":6,\"b\":22,\"c\":-8,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0081","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(-6)x²+(-17)x+(14)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-7/2, 2/3}","explanation_zh":"D=625；根={-7/2, 2/3}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034081,"parameters":{"a":-6,"b":-17,"c":14,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":-6,\"b\":-17,\"c\":14,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0082","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(6)x²+(12)x+(-18)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-3/1, 1/1}","explanation_zh":"D=576；根={-3/1, 1/1}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034082,"parameters":{"a":6,"b":12,"c":-18,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":6,\"b\":12,\"c\":-18,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0083","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(-6)x²+(-21)x+(-15)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-5/2, -1/1}","explanation_zh":"D=81；根={-5/2, -1/1}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034083,"parameters":{"a":-6,"b":-21,"c":-15,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":-6,\"b\":-21,\"c\":-15,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0084","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(6)x²+(16)x+(8)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-2/1, -2/3}","explanation_zh":"D=64；根={-2/1, -2/3}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034084,"parameters":{"a":6,"b":16,"c":8,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":6,\"b\":16,\"c\":8,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0085","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(-6)x²+(-11)x+(-3)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-3/2, -1/3}","explanation_zh":"D=49；根={-3/2, -1/3}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034085,"parameters":{"a":-6,"b":-11,"c":-3,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":-6,\"b\":-11,\"c\":-3,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0086","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(6)x²+(6)x+(0)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-1/1, 0/1}","explanation_zh":"D=36；根={-1/1, 0/1}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034086,"parameters":{"a":6,"b":6,"c":0,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":6,\"b\":6,\"c\":0,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0087","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(-6)x²+(-1)x+(1)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-1/2, 1/3}","explanation_zh":"D=25；根={-1/2, 1/3}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034087,"parameters":{"a":-6,"b":-1,"c":1,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":-6,\"b\":-1,\"c\":1,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0088","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(6)x²+(-4)x+(0)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{0/1, 2/3}","explanation_zh":"D=16；根={0/1, 2/3}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034088,"parameters":{"a":6,"b":-4,"c":0,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":6,\"b\":-4,\"c\":0,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0089","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(-6)x²+(9)x+(-3)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{1/2, 1/1}","explanation_zh":"D=9；根={1/2, 1/1}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034089,"parameters":{"a":-6,"b":9,"c":-3,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":-6,\"b\":9,\"c\":-3,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0090","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(6)x²+(0)x+(-6)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-1/1, 1/1}","explanation_zh":"D=144；根={-1/1, 1/1}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034090,"parameters":{"a":6,"b":0,"c":-6,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":6,\"b\":0,\"c\":-6,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0091","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(-6)x²+(5)x+(6)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-2/3, 3/2}","explanation_zh":"D=169；根={-2/3, 3/2}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034091,"parameters":{"a":-6,"b":5,"c":6,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":-6,\"b\":5,\"c\":6,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0092","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(6)x²+(-10)x+(-4)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-1/3, 2/1}","explanation_zh":"D=196；根={-1/3, 2/1}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034092,"parameters":{"a":6,"b":-10,"c":-4,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":6,\"b\":-10,\"c\":-4,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0093","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(-6)x²+(15)x+(0)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{0/1, 5/2}","explanation_zh":"D=225；根={0/1, 5/2}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034093,"parameters":{"a":-6,"b":15,"c":0,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":-6,\"b\":15,\"c\":0,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0094","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(6)x²+(-20)x+(6)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{1/3, 3/1}","explanation_zh":"D=256；根={1/3, 3/1}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034094,"parameters":{"a":6,"b":-20,"c":6,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":6,\"b\":-20,\"c\":6,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0095","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(-6)x²+(25)x+(-14)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{2/3, 7/2}","explanation_zh":"D=289；根={2/3, 7/2}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034095,"parameters":{"a":-6,"b":25,"c":-14,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":-6,\"b\":25,\"c\":-14,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0096","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(6)x²+(-30)x+(24)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{1/1, 4/1}","explanation_zh":"D=324；根={1/1, 4/1}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034096,"parameters":{"a":6,"b":-30,"c":24,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":6,\"b\":-30,\"c\":24,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0097","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(-6)x²+(21)x+(27)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-1/1, 9/2}","explanation_zh":"D=1089；根={-1/1, 9/2}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034097,"parameters":{"a":-6,"b":21,"c":27,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":-6,\"b\":21,\"c\":27,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0098","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(6)x²+(-26)x+(-20)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-2/3, 5/1}","explanation_zh":"D=1156；根={-2/3, 5/1}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034098,"parameters":{"a":6,"b":-26,"c":-20,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":6,\"b\":-26,\"c\":-20,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0099","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(-6)x²+(31)x+(11)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{-1/3, 11/2}","explanation_zh":"D=1225；根={-1/3, 11/2}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034099,"parameters":{"a":-6,"b":31,"c":11,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":-6,\"b\":31,\"c\":11,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r04-quadratic-equation-0100","batch_id":"batch-20261003-r04-quadratic-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-equation"],"title_zh":"二次方程式的精確根集合","stem_zh":"在實數論域，(6)x²+(-36)x+(0)=0 的 a≠0 且 D 為非負完全平方數。求最簡正分母、遞增且重複只列一次的根集合。","answer":{"kind":"expression","value":"{0/1, 6/1}","explanation_zh":"D=1296；根={0/1, 6/1}。用 (-b±√D)/(2a) 得精確有理根，再排序並合併重根；不用浮點比較。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["二次方程式的精確根集合"]},"variant":{"family_id":"qf-quadratic-exact-roots","seed":202610034100,"parameters":{"a":6,"b":-36,"c":0,"domain":"reals","operation":"exact_roots","semantic_template":"qf-quadratic-exact-roots/{\"a\":6,\"b\":-36,\"c\":0,\"domain\":\"reals\",\"operation\":\"exact_roots\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}