Question

If the roots of a quadratic equation $2x^2+5x+3k=0$ is reciprocal to other then find the values of k.

• A. $k=\frac{3}{2}$
  
• B. $k=-\frac{3}{2}$
  
• C. $k=-\frac{2}{3}$
  
• D. $k=\frac{2}{3}$
  

Answer 1

Answer: (D)

$k=\frac{2}{3}$

We have,

$2x^2+5x+3k=0$

Let the roots be $\alpha ,\frac{1}{\alpha }$.

So,

$\alpha \times \frac{1}{\alpha }=\frac{3k}{2}$

$\frac{3k}{2}=1$

$k=\frac{2}{3}$

Hence, this is the answer.