If one root of the equation $(k^{2} + 1) x^{2} + 13 x + 4 k = 0$ is reciprocal of the other, then $k$ has the value

- 2 + \sqrt{3}

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2 - \sqrt{3}

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Solution

The correct option is B $2 - \sqrt{3}$
$(k^{2} + 1) x^{2} + 13 x + 4 k = 0$
Let $a$ and $\frac{1}{a}$ be the roots
Products of the roots $= 1 = \frac{4 k}{k^{2} + 1}$
$\Rightarrow k^{2} - 4 k + 1 = 0$
$\Rightarrow k = 2 \pm \sqrt{3}$
Ans: B

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