Quadratics

Connect quadratic equations with their factors, roots and formula, and select an efficient solving method.

Curriculum rangeYears 9–11

Pick two whole-number roots — every method below finds the same two answers.

Root 1

Root 2

$x^2 - 8x + 12 = 0$

Method 1 — factorising

$(x - 2)(x - 6) = 0$

$x = 2$ or $x = 6$

Method 2 — the quadratic formula

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

$x = \frac{8 \pm 4}{2} = 4 \pm 2$

$x = 2$ or $x = 6$

Method 3 — completing the square

$(x - 4)^2 = 4$

$x = 4 \pm 2$

$x = 2$ or $x = 6$