Solve the given quadratic equation by factorization
$9 x^{2} - 3 x - 2 = 0$

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Solution

Given : $9 x^{2} - 3 x - 2 = 0$
$\Rightarrow 9 x^{2} - 6 x + 3 x - 2 = 0$
$\Rightarrow 3 x (3 x - 2) + 1 (3 x - 2) = 0 \Rightarrow (3 x - 2) (3 x + 1) = 0$
$\Rightarrow 3 x - 2 = 0 o r 3 x + 1 = 0$
$\Rightarrow x = \frac{2}{3} o r x = - \frac{1}{3}$
Thus, $x = \frac{2}{3}$ and $x = - \frac{1}{3}$ are the two roots.

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