If one of the zeroes of the quadratic polynomial $f(x)=4 x^2$ $-8 k x-9$ is equal in magnitude but opposite in sign of the other, then find the value of k.
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If one of the zeroes of the quadratic polynomial $f(x)=4 x^2$ $-8 k x-9$ is equal in magnitude but opposite in sign of the other, then find the value of $k$.

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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, $\frac{8 k}{4}=0 \Rightarrow k=0$

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