The roots of the equation $a (x^{2} + 1) - (a^{2} + 1) x$ = 0 are

$a, \frac{1}{a}$

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a, 2a

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$a, \frac{1}{2 a}$

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- a , -2a

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Solution

The correct option is A
$a, \frac{1}{a}$

Equation $a (x^{2} + 1) - (a^{2} + 1) x$ = 0

⇒ $a x^{2} - (a^{2} + 1) x + a$ = 0

⇒ $(a x - 1) (x - a)$ = 0 ⇒ $x = a, \frac{1}{a}$

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