Find the roots of the equation $2 x^{2} + x - 6 = 0$ by factorisation.

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Solution

The given quadratic equation is
$2 x^{2} + x - 6 = 0$
$\Rightarrow 2 x^{2} + 4 x - 3 x - 6 = 0$
$\Rightarrow 2 x (x + 2) - 3 (x + 2) = 0$
$\Rightarrow (2 x - 3) (x + 2) = 0$
$\Rightarrow x = - 2, \frac{3}{2}$

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