28 Let $\alpha$ and $\beta$ be the roots of $x^{2}-4 x+c=0$, where $c$ is a real number. If $-\alpha$ is a root of $x^{2}+4 x-c=0$, find the value of $\alpha \beta$.
28. Answer: 0
$\alpha$ is a root of the equation $x^{2}-4 x+c=0$ so $\alpha^{2}-4 \alpha+c=0$ and $-\alpha$ is a root of the equation $x^{2}+4 x-c=0$ so $(-\alpha)^{2}+4(-\alpha)-c=0$. We have $2 c=0 \Rightarrow \alpha \beta=c$ $=0$.