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Discriminant

The values of...

Question

The value(s) of $a$ for which the roots of $2 x^{2} + (a^{2} - 1) x + a^{2} + 3 a + 4 = 0$ are reciprocal to each other is/are

- 1

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- 2

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Solution

The correct options are
A $- 1$
C $- 2$
$2 x^{2} + (a^{2} + 1) x + a^{2} + 3 a + 4 = 0$
Comparing with $a x^{2} + b x + c = 0$
The roots are reciprocal when $a = c$ , so we get
$\Rightarrow a^{2} + 3 a + 4 = 2 \Rightarrow a^{2} + 3 a + 2 = 0 \Rightarrow (a + 1) (a + 2) = 0 \Rightarrow a = - 1, - 2$

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