SOLUTION —
$f(x)=4 x^2-8 k x-9$
Let one of the zeroes of the polynomial be $\alpha$ and the other zeroes be $-\alpha$
$\begin{gathered}\text { Sum of zeroes }=\left(-\frac{b}{a}\right)=\frac{8 k}{4} \\\alpha+(-\alpha)=0\end{gathered}$
So, $\frac{8 k}{4}=0 \Rightarrow k=0$