On annulus containing all the zeros of a polynomial

Abstract

Recently Dalal and Govil [5] proved that, for any set of positive numbers {Ak}nk=1 such that Σnk=1 Ak = 1, a complex polynomial P(z) Σ nk=0dkzk (dk ≠ 0, 0≤ k ≤ n) has all its zeros in the annulus A = {z: r1 ≤ |z| ≤ r2}, where This paper presents the best possible results in the same direction by identifying the smallest annulus containing all the zeros of P(z). © 2014 Younseok Choo.