Find the value of k for which the roots of the equation

Question:

Find the value of $k$ for which the roots of the equation $3 x^{2}-10 x+k=0$ are reciprocal of each other.

 

Solution:

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

The given equation is $3 x^{2}-10 x+k=0$.

Product of roots $=\frac{k}{3}$

$\Rightarrow \alpha \times \frac{1}{\alpha}=\frac{k}{3}$

$\Rightarrow 1=\frac{k}{3}$

$\Rightarrow k=3$

Hence, the value of $k$ for which the roots of the equation $3 x^{2}-10 x+k=0$ are reciprocal of each other is 3 .

 

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