Solve the following quadratic equation: 4 x^2-2 (a^2+b^2 ) x+a^2 … - Vidyadip

Question

Solve the following quadratic equation:
$ 4 x^2-2\left(a^2+b^2\right) x+a^2 b^2=0 $

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Answer

$ 4 x^2-2\left(a^2+b^2\right) x+a^2 b^2=0 $
$ \Rightarrow 4 x^2-2 a^2 x-2 b^2 x+a^2 b^2=0 $
$ \Rightarrow 2 x\left(2 x-a^2\right)-b^2\left(2 x-a^2\right)=0 $
$ \Rightarrow\left(2 x-a^2\right)\left(2 x-b^2\right)=0 $
$ \Rightarrow\left(2 x-a^2\right)=0 \text { or }\left(2 x-b^2\right)=0$
$\Rightarrow\text{x}=\frac{\text{a}^2}{\text{2}}$ or $\text{x}=\frac{\text{b}^2}{\text{2}}$
Hence, $\frac{\text{a}^2}{\text{2}}$ and $\frac{\text{b}^2}{\text{2}}$ are the roots of the given equation.

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