Question

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

Answer 1

Find the value of $k$.

Given: One zero of $2x^2-3x+k$ is reciprocal to the other.

let $\alpha$ be the one root of the quadratic equation.

So, the other root will be $\frac{1}{\alpha }$.

We know that for the quadratic equation $a{x}^2+bx+c$ product of the roots is given by $\frac{c}{a}$.

Thus, the product of the roots of given quadratic equation $=\frac{k}{2}$.

$$\begin{gathered} \Rightarrow \alpha \times \frac{1}{\alpha }=\frac{k}{2} \\ \Rightarrow 2=k \\ \Rightarrow k=2 \end{gathered}$$

Hence, the value of $k$ is $2.$