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The roots of the equation $12 ab x^{2} - (9 a^{2} - 8 b^{2}) x - 6 ab = 0$ are [[1]] and [[2]].

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answer is 3 A 4 B, - 2 B 3 A.

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Detailed Solution

The roots of the equation

12 ab x^{2} - (9 a^{2} - 8 b^{2}) x - 6 ab = 0

are

\frac{3 a}{4 b}

and

- \frac{2 b}{3 a}

.
Given equation is,

12 ab x^{2} - (9 a^{2} - 8 b^{2}) x - 6 ab = 0

Then,

12 ab x^{2} - (9 a^{2} - 8 b^{2}) x - 6 ab = 0

⟹ 12 ab x^{2} - 9 a^{2} x + 8 b^{2} x - 6 ab = 0

⟹ 3 ax (4 bx - 3 a) + 2 b (4 bx - 3 a) = 0

⟹ (3 ax + 2 b) (4 bx - 3 a) = 0

⟹ 3 ax + 2 b = 0 or 4 bx - 3 a = 0

⟹ 3 ax = - 2 b or 4 bx = 3 a

⟹ x = - \frac{2 b}{3 a} or x = \frac{3 a}{4 b}

Therefore,

- \frac{2 b}{3 a} and \frac{3 a}{4 b}

are the roots of the equation

12 ab x^{2} - (9 a^{2} - 8 b^{2}) x - 6 ab = 0

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