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Question 28472: Validity of a Quadratic-Equation Form

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0055-28472 · q-20261003-r04-quadratic-equation-0022

Original question and givens

Over the reals, is (-1)x²+(9)x+(-3)=0 a quadratic equation in one variable? Answer Yes or No.

  • G001 — Over the reals, is (-1)x²+(9)x+(-3)=0 a quadratic equation in one variable? Answer Yes or No.

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

Step-by-step derivation

S001 · implies

Before

source roles = [qf-quadratic-form-validity, quadratic_form]

After

derived = [[quadratic_eligibility_yes_no]]

Conditions: none

List this scalar/label/set/point answer role or mode-specific ordered fields,not an imposed universal tuple.Retain legacy domain/underscore operation and integer fractions with/1;original bilingual snapshots stay unchanged.

Step identifiers and dependencies

Rule: source_answer_roles_or_ordered_fields_without_JS · Uses: G001

S002 · implies

Before

source roles = [-1, 9, -3]

After

derived = [Yes, Yes]

Conditions: none

Only a!=0 is quadratic.Here a0 is a legal eligibilityNo and may leave a linear,constant or zero expression;do not apply the quadratic formula.

Step identifiers and dependencies

Rule: Legacy_quadratic_ELIGIBILITY_a0_legalNo_NOT_formula_application · Uses: G001, S001

Reverse checks

  • S002 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.
  • S001 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.

Result

Yes

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: 304a6e0990812570280f925b5bcef3d1703d9c10c89e81f459815a0e3d97b3c2
  • candidate record SHA-256: 40e82a8c08efed6aded6a9418f8940ab7851eae713e2a3f53d83f327ab20985f
  • semantic review receipt SHA-256: 6af367dae24a584f3596525c4953bbc2115343efd68cc9083693eb5c1ef2e683
  • question-first witness SHA-256: 611eb69f3716404b968296a8b0d7d8c61b5ca18129d406f1ff9c7c11e10ffb4e
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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