Plane curves and p-adic roots of unity

We prove the following result: Let f(x,y) be a polynomial of degree d in two variables whose coefficents are integers in an unramified extension of Q(p). Assume that the reduction of f module p is irreducible of degree d and not a binomial. Assume also that p > d(2) + 2. Then the number of solutions of the inequality \f(zeta(1),zeta(2))\ < p(-1), with zeta(1), zeta(2) roots of unity in <(Q(p))over bar> or zero, is at most pd(2).