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Solving quadratic equations by factorising
The null factor law, solving ax² + bx = 0, x² − d = 0, monic and non-monic trinomial equations, and rearranging to equal zero first.
Null factor law
Solve $x^2 - 5x = 0$.
$x(x - 5) = 0$
$x = 0$ or $x = 5$
Solve $x^2 + x - 12 = 0$.
$(x + 4)(x - 3) = 0$
$x = -4$ or $x = 3$
Solve $2x^2 = 7x - 3$.
$2x^2 - 7x + 3 = 0$
$(2x - 1)(x - 3) = 0$, so $x = \tfrac{1}{2}$ or $x = 3$.
Null factor law
$ab = 0 \Rightarrow a = 0$ or $b = 0$
$x^2 - 16 = 0$
$x = \pm 4$
$(x - 3)^2 = 0$
$x = 3$ (one solution)
Solve $x^2 - 5x = 0$. Enter both solutions.
$x(x - 5) = 0$.
Solve $x^2 + x - 12 = 0$.
$(x + 4)(x - 3) = 0$.
Solve $2x^2 = 7x - 3$.
$(2x - 1)(x - 3) = 0$.
Solve $x^2 - 16 = 0$.
$(x - 4)(x + 4) = 0$.
Solve $x^2 = 6x - 9$.
$(x - 3)^2 = 0$.
Solve $x^2 - 7x + 10 = 0$.
$(x - 2)(x - 5) = 0$.
Solve $2x^2 + 6x = 0$.
$2x(x + 3) = 0$.
Solve $x^2 + 8x + 12 = 0$.
$(x + 2)(x + 6) = 0$.
New numbers every time. Keep going until you get five in a row.