# The Red Capes are coming!

Algebra Level 5

$\begin{cases} a+b+c= 0 \\ a^5 + b^5 + c^5 = 5 \\ a^6 + b^6 + c^6 = 6 \end{cases}$

Let $$a,b$$ and $$c$$ be numbers satisfying the system of equations above. And at least one of $$a,b$$ and $$c$$ is not a real number.

Given that $$a^2+b^2+c^2$$ satisfy a least degree monic polynomial $$f(X)$$, find $$f(2)$$.

×