Question

If one zero of $2x^2-3x+m$ is reciprocal to the other then the value of m is

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

Answer 1

The correct option is A $2$

Let the roots of the polynomials are $\alpha$ and $\beta$

according to the question one root is reciprocal to other then $\beta =\frac{1}{\alpha }$

$\therefore$Product of the root=$\frac{constantterm}{coefficientof{x}^2}$

$\Rightarrow \alpha \times \beta =\frac{m}{2}$

$\Rightarrow \alpha \times \frac{1}{\alpha }=\frac{m}{2}$

$\Rightarrow m=2$