Question

If one root of the quadratic equation $3x^2+5a^{2}x+k=0$ is twice the reciprocal of the other root, then the value of $k$ is equal to

• A. $3$
• B. $6$
• C. $5a^2$
• D. $1$

Answer 1

The correct option is B $6$

Let $\alpha$ be a root of the quadratic equation $3x^2+5a^{2}x+k=0$
Then, the other root will be $\frac{2}{\alpha }$
Now, product of roots $=\alpha \times \frac{2}{\alpha }$
$\Rightarrow \alpha \times \frac{2}{\alpha }=\frac{k}{3}$
$\Rightarrow k=6$
Hence, the correct answer is option (2).