Question

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

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

Answer 1

The correct option is A 2

Let $\alpha$ be the first root of the polynomial $2x^2-3x+k$.
Then according to question other root is $\frac{1}{\alpha }.$
Now, product of roots=$\frac{constantterm}{coefficientof{x}^2}$
$\Rightarrow \alpha \times \frac{1}{\alpha }=\frac{k}{2}$
$\Rightarrow k=2$
Option A is correct.