Consider a degree $n$ polynomial $P(x)$ with coefficients $c_i \in \{-1,0,1\}$ chosen uniformly and independently.
What is the probability that $P(x)$ has a root which is a root of unity?
Previously asked at http://math.stackexchange.com/questions/798082/probability-a-polynomial-has-a-root-which-is-a-root-of-unity
