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Solving a Quadratic Equation by Factorization Method

Solve the fol...

Question

Solve the following quadratic equation by factorization method
$9 x^{2} - 9 (a + b) x + (2 a^{2} + 5 a b + 2 b^{2}) = 0$

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Solution

$9 x^{2} - 9 (a + b) x + (2 a^{2} + 5 a b + 2 b^{2}) = 0$
$\Rightarrow 9 x^{2} - 9 (a + b) x + 2 a^{2} + 4 a b + a b + 2 b^{2} = 0$
$\Rightarrow 9 x^{2} - 9 (a + b) x + 2 a (a + 2 b) + b (a + 2 b) = 0$
$\Rightarrow 9 x^{2} - 9 (a + b) x + (2 a + b) (a + 2 b) = 0$
$\Rightarrow 9 x^{2} - 3 (2 a + b) x - 3 (a + 2 b) x + (2 a + b) (a + 2 b) = 0$
$\Rightarrow 3 x (3 x - [2 a + b]) - (a + 2 b) [3 x - [2 a + b]] = 0$
$\Rightarrow [3 x - (a + 2 b)] [3 x - (2 a + b)] = 0$

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