On solving the following quadratic equation by factorization, the roots are $\frac{2 b}{a}, \frac{b}{a}$ :
$a^{2} x^{2} - 3 a b x + 2 b^{2} = 0$

True

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False

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Solution

The correct option is A True
$a^{2} x^{2} - 3 a b x + 2 b^{2} = 0$
$\Rightarrow$ $a^{2} x^{2} - 2 a b x - a b x + 2 b^{2} = 0$
$\Rightarrow$ $a x (a x - 2 b) - b (a x - 2 b) = 0$
$\Rightarrow$ $(a x - 2 b) (a x - b) = 0$
$\Rightarrow$ $a x - 2 b = 0$ and $a x - b = 0$
$\Rightarrow$ $x = \frac{2 b}{a}$ and $x = \frac{b}{a}$

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a^{2} x^{2} - 3 a b x + 2 b^{2}

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