# Cosines and polynomials?

Algebra Level 5

If $$\cos \left( \frac {720^\circ}{7} \right)$$ is a root of the sixth-degree polynomial

$ax^{6}-bx^{4}+cx^{2}-x-1$

where $$a, b, c$$ are positive integers, find $$a+b+c$$.

Bonus: Can you find the monic third degree polynomial with rational coefficients that has $$\cos (\frac {720^\circ}{7})$$ as a root?

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