Question:
If one zero of the quadratic polynomial $1(x)=4 x^{2}-8 k x-9$ is negative of the other, find the value of $k$.
Solution:
Since $\alpha$ and $-\alpha$ are the zeros of the quadratic polynomial $f(x)=4 x^{2}-8 k x-9$
$\alpha-\alpha=0$
$\frac{-\text { Coefficient of } x}{\text { Coefficient of } x^{2}}=0$
$\frac{-8 k}{4}=0$
$-8 k=0 \times 4$
$-8 k=0$
$k=\frac{0}{-8}$
$k=0$
Hence, the Value of $k$ is 0 .
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