In this paper, Mahler provides inequalities relating length (the sum of the absolute values of the coefficients), Mahler measure, discriminant and minimal distance between zeros of a polynomial. In particular, he gives an upper bound on the absolute value of the discriminant and a lower bound for the minimal distance between zeros. \par Reprint of the author's paper [Mich. Math. J. 11, 257--262 (1964; Zbl 0135.01702)].