HMMT-Nov 2009 guts, Problem 25

Find all solutions to $x^{4}+2 x^{3}+2 x^{2}+2 x+1=0$ (including non-real solutions).

Solution: We can factor the polynomial as $(x+1)^{2}\left(x^{2}+1\right)$. $\fbox{-1, i,-i}$.

Answer: -1, i,-i