# Not Just Vieta's Derivatives!

Algebra Level 5

$\begin{eqnarray} P(x) &=& x^{6} - x^{5} - x^{3} - x^{2} - x \\ Q(x) &=& x^{4} - x^{3} - x^{2} - 1 \\ \end{eqnarray}$

Consider the polynomials above.

Given that $$z_{1},z_{2},z_{3},$$and $$z_{4}$$ are the roots of $$Q(x) = 0$$, find $$P(z_{1}) + P(z_{2}) + P(z_{3}) + P(z_{4})$$.

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