of Polynomials H. A. Soleiman Mezerji and M. Bidkham Received: July 16, 2013; Accepted: January 10, 2014 Abstract. Let p(z) be a polynomial with complex coefficients. In this paper, we obtain some new results concerning the location of zeros of polynomials p(z). Our results sharpened Cauchy's result, along with some of the other known results, which were based on the classical Cauchy's work. Finally, we prove the results concerning the bounds for the number of zeros for the polynomial p(z), which generalize some known results. Keywords: Cauchy theorem; Eneström-Kakeya theorem; zeros. AMS Subject classification: Primary: 30C10, 30C15 Version to read: PDF ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2014, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |