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Solve the following quadratic equations by factorization:

$a x 2 + 1 − x a 2 + 1 = 0$

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a, 1 a

a, 2 a

1, 1 a

1, 2 a

answer is C.

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Detailed Solution

Given:

a x 2 + 1 − x a 2 + 1 = 0 ⇒ a x 2 + a − x a 2 + 1 = 0 ⇒ a x 2 − x a 2 + 1 + a = 0 ⇒ a x 2 − a 2 + 1 x + a = 0

⇒ a x 2 − a 2 x − x + a = 0 ⇒ a x (x − 1) − 1 (x − a) = 0 ⇒ (x − 1) (a x − 1) = 0 ⇒ x − 1 = 0 or a x − 1 = 0 ⇒ x = 1, 1 a

Hence, the roots of the given equation are 1 and

\frac{1}{a}

.
Thus, the correct option is 3.

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