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?
by
Joel Tan