Topic summary · IGCSE handout

Quadratic Equations summary

Quadratics solve by factorising, completing the square, or the quadratic formula. Sketching links roots to intercepts.

Open Learning Sheet — Quadratic Equations Download Quadratic Equations answers PDF

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Key learning points

Factorise when integer roots are likely; formula always works.
$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ ; discriminant $b^2-4ac$ counts real roots.
Expand to check factorisation.

Worked example 1 — Factorise and solve

Solve $x^2-5x+6=0$ .

Working

(x-2)(x-3)=0\Rightarrow x=2\text{ or }3

Factor pairs.

Worked example 2 — Quadratic formula

Solve $x^2+2x-5=0$ in surd form.

Working

x=-1\pm\sqrt{6}

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ .

Worked example 3 — Completing the square

Write $x^2+6x+5$ in completed-square form.

Working

(x+3)^2-4

Half of 6 is 3.

Scaffolded Learning Sheet and answers (PDFs)

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Open Learning Sheet Answers PDF

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