  Let $c_1(x),c_2(x),f_1(x),f_2(x)$ be polynomials with rational coefficients.
With obvious exceptions, there can be at most finitely many roots of unity
among the zeros of the polynomials $c_1(x)f_1(x)^n+c_2(x)f_2(x)^n$ with
$n=1,2\ldots$. We estimate the orders of these roots of unity in terms of the
degrees and the heights of the polynomials $c_i$ and $f_i$.
