Question:
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 $k$.
Solution:
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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