If one root of $6 x^{2} + 13 x + b + 1 = 0$ is the reciprocal of the other root, then the value of $b$ is

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Solution

$6 x^{2} + 13 x + b + 1 = 0$
Let the roots be $α$ and $\frac{1}{α}$
So, product of roots is,
$α \times \frac{1}{α} = \frac{b + 1}{6}$
$\Rightarrow b + 1 = 6$
$\Rightarrow b = 5$

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