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Which of the below is a root of the following quadratic equation?

$9 x 2 − 6 b 2 x − a 4 − b 4 = 0$

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a 2 + b 2 3

a 2 + b 2 4

a 2 + 2 b 2 4

2 a 2 + 2 b 2 18

answer is A.

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Detailed Solution

Given: The quadratic equation

9 x 2 − 6 b 2 − a 4 − b 4 = 0

The constant term

⇒ a 4 − b 4 = a 2 − b 2 a 2 + b 2

The coefficient of middle term

⇒ − 6 b 2 = − 3 a 2 + b 2 + 3 a 2 − b 2

The quadratic equation can be rewritten as:
Question Image

The roots of the quadratic equation 9 x 2 − 6 b 2 − a 4 − b 4 = 0 are a 2 + b 2 3 and a 2 − b 2 3

. Hence, the correct option is 1.

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