Question:
Very-Short-Answer Questions
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.
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