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All 5 lessons in Quadratic Equations II

  1. 1. Reading the Hidden Numbers — Extracting the Sum and Product of Roots

    Apply the formulas α + β = −b/a and αβ = c/a to extract the sum and product of roots from any quadratic equation without solving it

  2. 2. Building the Equation — Constructing a Quadratic from Sum and Product of Roots

    Use the template x² − (α + β)x + αβ = 0 to construct a quadratic equation from given roots or from their sum and product, clearing fractions to reach integer coefficients

  3. 3. The Symmetric Toolkit — Evaluating Root Expressions Without Solving

    Derive and apply the five core symmetric identities to evaluate expressions in α and β using only the sum S and product P from any quadratic equation

  4. 4. The Full Synthesis — Forming New Equations from Transformed Roots

    Apply a five-step master method to derive new quadratic equations when roots are scaled, inverted, translated, or squared — using only S and P from the original equation

  5. 5. From Sentences to Equations — Word Problems Leading to Quadratic Equations

    Apply a four-step translation protocol to convert number, age, area, and speed word problems into quadratic equations, and reject extraneous solutions using real-world constraints

Unit code SSA7