Solve the following quadratic equation by factorization, the roots are :
$9 x^{2}$ - 3x - 2 = 0

\frac{2}{3}, - \frac{1}{6}

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\frac{2}{5}, - \frac{1}{3}

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\frac{1}{3}, - \frac{1}{3}

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\frac{2}{3}, - \frac{1}{3}

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Solution

The correct option is D $\frac{2}{3}, - \frac{1}{3}$
$9 x^{2} - 3 x - 2 = 0$
$\Rightarrow$ $9 x^{2} - 6 x + 3 x - 2 = 0$
$\Rightarrow$ $3 x (3 x - 2) + 1 (3 x - 2) = 0$
$\Rightarrow$ $(3 x - 2) (3 x + 1) = 0$
$\Rightarrow$ $3 x - 2 = 0$ and $3 x + 1 = 0$
$\Rightarrow$ $x = \frac{2}{3}$ and $x = - \frac{1}{3}$
$∴$ The roots of the equation $9 x^{2} - 3 x - 2 = 0$ are $\frac{2}{3}, - \frac{1}{3}$

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