The roots of the quadratic equation ${a b x}^{2} + (b^{2} - a c) x - b c = 0$ are

\frac{c}{b}, \frac{b}{a}

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\frac{c}{b}, - \frac{b}{a}

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- \frac{c}{b}, \frac{b}{a}

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- \frac{c}{b}, - \frac{b}{a}

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Solution

The correct option is A $\frac{c}{b}, - \frac{b}{a}$
Given equation is:
$a b x^{2} + (b^{2} - a c) x - b c = 0$
$∴ {a b x}^{2} + b^{2} x - a c x - b c = 0$
$\Rightarrow b x (a x + b) - c (a x + b) = 0$
$\Rightarrow (b x - c) (a x + b) = 0$
$\Rightarrow x = \frac{c}{b}, - \frac{b}{a}$

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