Solve the following quadratic equation:12abx^2 - (9a^2 - 8b^2)x -… - Vidyadip

Question

Solve the following quadratic equation:$12abx^2 - (9a^2 - 8b^2)x - 6ab = 0$

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Answer

$12abx^2 - (9a^2 - 8b^2)x - 6ab = 0$
$\Rightarrow 12abx^2 - 9a^2x + 8b^2x - 6ab = 0$
$\Rightarrow 3ax(4bx - 3a) + 2b(4bx - 3a) = 0$
$\Rightarrow (4bx - 3a)(3ax + 2b) = 0$
$\Rightarrow (4bx - 3a) = 0 or (3ax + 2b) = 0$
$\Rightarrow 4bx = 3a or 3ax = -2b$
$\Rightarrow\text{x}=\frac{\text{3a}}{\text{4b}}$ or $\text{x}=\frac{-\text{2b}^2}{\text{3a}}$
Hence, $\frac{\text{3a}}{\text{4b}}$ and $\frac{-\text{2b}}{\text{3a}}$ are the roots of the given equation.

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