On the Zeros of Polynomials with Restricted Coefficients

Abstract

Abstract Let P ( z ) = ∑ j = 0 n a j z j P\left( z \right) = \sum\nolimits_{j = 0}^n {{a_j}{z^j}} be a polynomial of degree n such that a n ≥ a n− 1 ≥ . . . ≥ a 1 ≥ a 0 ≥ 0. Then according to Eneström-Kakeya theorem all the zeros of P ( z ) lie in |z| ≤ 1. This result has been generalized in various ways (see [1, 3, 4, 6, 7]). In this paper we shall prove some generalizations of the results due to Aziz and Zargar [1, 2] and Nwaeze [7].