Question:

If one root of the quadratic equation $3 x^{2}-10 x+k=0$ is reciprocal of the other, find the value of $k$.

Solution:

Let $\alpha$ and $\beta$ be the roots of the equation $3 x^{2}-10 x+k=0$.

$\therefore \alpha=\frac{1}{\beta}$         (Given)

$\Rightarrow \alpha \beta=1$

$\Rightarrow \frac{k}{3}=1 \quad$ (Product of the roots $=\frac{c}{a}$ )

$\Rightarrow k=3$

Hence, the value of k is 3.