Question

If one zero of the quadratic polynomial $p\left(x\right)=4x^2-8xk-9$ is negative of the other, find the value of $k$.

Answer 1

Find the value of $k$.

Given: One zero of $p\left(x\right)=4x^2-8xk-9$ is negative to the other

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

So, the other root will be $-\alpha$.

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

Thus, sum of the roots of the given quadratic equation $=\frac{8k}{4}$.

$$\begin{gathered} \Rightarrow \frac{8k}{4}=\alpha +\left(-\alpha \right) \\ \Rightarrow 2k=0 \\ \Rightarrow k=0 \end{gathered}$$

Hence, the value of $k$ is $0$.