On roots of polynomials with positive coefficients

Let ? be an algebraic number with no nonnegative conjugates over the field of the rationals. Settling a recent conjecture of Kuba, Dubickas proved that the number ? is a root of a polynomial, say P, with positive rational coefficients. We give in this note an upper bound for the degree of P in terms of the discriminant, the degree and the Mahler measure of ?; this answers a question of Dubickas.