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

Question

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

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Answer

$4x^2 - 2(a^2 + b^2)x + a^2b^2 = 0$
$\Rightarrow 4x^2 - 2a^2x - 2b^2x + a^2b^2 = 0$
$\Rightarrow 2x(2x - a^2) - b^2(2x - a^2) = 0$
$\Rightarrow (2x - a^2)(2x - b^2) = 0$
$\Rightarrow (2x - a^2) = 0$ or $(2x - b^2) = 0$
$\Rightarrow\text{x}=\frac{\text{a}^2}{\text{2}}$ 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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