FP1.2 - Roots of quadratic equations

Sum of roots and product of roots For the equation ax2 + bx + c = 0, whose roots are α and β, of a quadratic equation. b c then α + β = −, αβ =. a a.

Use fp1.2.1 - sum of roots and product of roots to connect the rule to the data and decision in the question.

This matters because fp1.2.1 - sum of roots and product of roots determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp1.2.1 - sum of roots and product of roots to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP1.2.1 - Sum of roots and product of roots is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Manipulation of expressions Knowledge of the identity α3 + β3 ≡ (α + β)3 − 3αβ(α + β). involving the sum of roots and product of roots.

Use fp1.2.2 - manipulation of expressions to connect the rule to the data and decision in the question.

This matters because fp1.2.2 - manipulation of expressions determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp1.2.2 - manipulation of expressions to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP1.2.2 - Manipulation of expressions is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Forming quadratic equations with 1 1 1 1 2 For example, with roots α3, β3;,;,; α +, new roots. α β α2 β2 β β +; etc. α.

Use fp1.2.3 - forming quadratic equations with 1 1 1 1 2 to connect the rule to the data and decision in the question.

This matters because fp1.2.3 - forming quadratic equations with 1 1 1 1 2 determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp1.2.3 - forming quadratic equations with 1 1 1 1 2 to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: use the formula and units given in the question, show the substitution and interpret the result; the calculation alone is not the conclusion.