Question 1(ii)
Find the roots of the following quadratic equations by factorisation:
(ii) $2 x^{2} + x - 6 = 0$

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Solution

(ii)
$2 x^{2} + x - 6$
$= 2 x^{2} + 4 x - 3 x - 6$
(Splitting the middle term x as 4x-3x because $4 x \times - 3 x = - 12 x^{2}$ )
$= 2 x (x + 2) - 3 (x + 2) = (x + 2) (2 x - 3)$
Roots of this equation are the values for which $(x + 2) (2 x - 3) = 0$
$∴ x + 2 = 0 o r 2 x - 3 = 0 \Rightarrow x = - 2 o r x = \frac{3}{2}$

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