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Zeroes of a Polynomial

Solve the giv...

Question

Solve the given quadratic equation by factorization method
$x^{2} - 4 a x + (4 a^{2} - b^{2}) = 0$

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Solution

We have
$x^{2} - 4 a x + (4 a^{2} - b^{2}) = 0$

Here, Constant term $= (4 a^{2} - b^{2}) = (2 a - b) (2 a + b)$

and coefficient of middle term $= - 4 a$

Also. Coefficient of middle term $= - [(2 a - b) + (2 a + b)]$

$∴ x^{2} - {(2 a - b) + (2 a + b)} x + (2 a - b) (2 a + b) = 0$

$\Rightarrow x {x - (2 a - b)} - (2 a + b) {x - (2 a - b)} = 0 \Rightarrow {x - (2 a - b)} {x - (2 a + b)} = 0$

$\Rightarrow x - (2 a - b) = 0 o r x - (2 a + b) = 0 \Rightarrow x = 2 a - b o r x = 2 a + b$

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