Question:
If one root of $5 x^{2}+13 x+k=0$ be the reciprocal of the other root, then the value of $k$ is
(a) 0
(b) 1
(c) 2
(d) 5
Solution:
(d) 5
Let the roots of the equation $\left(5 x^{2}+13 x+k=0\right)$ be $\alpha$ and $\frac{1}{\alpha}$.
$\therefore$ Product of the roots $=\frac{c}{a}$
$\Rightarrow \alpha \times \frac{1}{\alpha}=\frac{k}{5}$
$\Rightarrow 1=\frac{k}{5}$
$\Rightarrow k=5$
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