Solve the following quadratic equation: a b x^2+ (b^2-a c ) x-b c… - Vidyadip

Question

Solve the following quadratic equation:
$ a b x^2+\left(b^2-a c\right) x-b c=0 $

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Answer

$ a b x^2+\left(b^2-a c\right) x-b c=0 $
$ \Rightarrow 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(a x+b)(b x+c)=0 $
$ \Rightarrow(a x+b)=0 \text { or }(b x-c)=0$
$\Rightarrow\text{x}=\frac{-\text{b}}{\text{a}}$ or $\text{x}=\frac{\text{c}}{\text{b}}$
Hence, $\frac{-\text{b}}{\text{a}}$ and $\frac{\text{c}}{\text{b}}$ are the roots of the given equation.

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