If one root of the equation


If one root of the equation $5 x^{2}+13 x+k=0$ is the reciprocal of the other root then find the value of $k$.



Let one root be $\alpha$ and the other root be $\frac{1}{\alpha}$.

The given equation is $5 x^{2}+13 x+k=0$.

Product of roots $=\frac{k}{5}$

$\Rightarrow \alpha \times \frac{1}{\alpha}=\frac{k}{5}$

$\Rightarrow 1=\frac{k}{5}$

$\Rightarrow k=5$

Hence, the value of k is 5.


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