17. [10] Let $p(x)=x^{2}-x+1$. Let $\alpha$ be a root of $p(p(p(p(x)))$. Find the value of
$$
(p(\alpha)-1) p(\alpha) p(p(\alpha)) p(p(p(\alpha))
$$
Answer:
$$
-1
$$

Since $(x-1) x=p(x)-1$, we can set
$$
\begin{aligned}
(p(\alpha)-1) p(\alpha) p(p(\alpha)) p(p(p(\alpha)) & =(p(p(\alpha))-1) p(p(\alpha)) p(p(p(\alpha)) \\
& =(p(p(p(\alpha)))-1) p(p(p(\alpha)) \\
& =p(p(p(p(\alpha))))-1 \\
& =-1
\end{aligned}
$$