Using the factorisation method, find the roots of the following quadratic equation: $x^{2} - 10 x + 24 = 0$

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Solution

$x^{2} - 10 x + 24 = 0$
$\Rightarrow x^{2} - 10 x + (2 \times 2 \times 2 \times 3) = 0$
$\Rightarrow x^{2} - 10 x + (6 \times 4) = 0$
$\Rightarrow x^{2} - 6 x - 4 x + (6 \times 4) = 0$
$\Rightarrow x (x - 6) - 4 (x - 6) = 0$
$\Rightarrow (x - 4) (x - 6) = 0$
$\Rightarrow x = 4, 6$

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