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

The question says one root is negative of others.

So, the sum of the roots must be zero.

For any quadratic equation

Like : $a{x}^2+bx+c=0$

The sum of roots is given by $\frac{-b}{a}$

So, in this equation : $4x^2-8ka-9$

$b=-8k$ & $a=4$

So, $0=\frac{-b}{a}$

$\frac{-(-8k)}{4}=0$

$2k=0\Rightarrow k=0$