A note on the zeros of polar derivative of a polynomial with complex coefficients

Abstract

According to the Enestrom-Kakeya theorem “zeros of the polynomial whose coefficients are positive, real and increasing along with the powers of the variable are lie in the unit circle” see [6, 10]. In [1], Aziz and Mahammad, showed that zeros of f(z) satisfies |z| ≥ n/n+1 are simple, under the same conditions. This article shows that the result of Gulzar, Zargar and Akthar in [8] is simplified in terms of real and imaginary parts of complex coefficients of the polynomial, also it extends some generalizations by imposing conditions on hypothesis in different ways.