American Journal of Mathematical Analysis
ISSN (Print): 2333-8490 ISSN (Online): 2333-8431 Website: http://www.sciepub.com/journal/ajma Editor-in-chief: Apply for this position
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American Journal of Mathematical Analysis. 2014, 2(2), 23-27
DOI: 10.12691/ajma-2-2-2
Open AccessArticle

On Location of Zeros of Polynomials

M S PUKHTA1,

1Division of Agri. Statistics, Sher-e-Kashmir, University of Agricultural Sciences and Technology of Kashmir, India

Pub. Date: May 25, 2014

Cite this paper:
M S PUKHTA. On Location of Zeros of Polynomials. American Journal of Mathematical Analysis. 2014; 2(2):23-27. doi: 10.12691/ajma-2-2-2

Abstract

If be a polynomial of degree n such that aj=aj+ibj where aj and bj, j = 0, 1, ….., n are real numbers. In this paper we obtain a generalization of well known result of Eneström -Kakeya concerning the bounds for the moduli of the zeros of polynomials with complex coefficients which improve upon some results due to A. Aziz and Q.G Mohammad and others.

Keywords:
complex polynomials zeros Eneström – Kakeya Theorem

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References:

[1]  A. Aziz and Q. G. Mohammad, Zero free regions for polynomials and some generalizations of Enström-Kakeya theorem, Cand. Math. Bull., 27(1984), 265-272.
 
[2]  G. Eneström, Remarqueesur un Theoremerelatif aux racines de I’ equation anxn + an-1xn-1 + ……+ a0 = 0 outous les coefficients sont reels et possitifs, Tôhoku Math. J., 18 (1920), 34-36.
 
[3]  A. Hurwitz, Űberdie Nullslenllen der Bessel Schen Function, Math. Ann., 33(1989)246-266.
 
[4]  A.Joyal, G.Labelle and Q.I. Rahman, On the location of zeros of polynomials, Canad. Math. Bull., 10 (1967), 53-63.
 
[5]  S.Kakeya, On the limits of the roots of an algebraic equation with positive coefficients, Tôhoku Math. J., 2 (1912-13), 140-142.
 
[6]  A. Aziz and B. A. Zargar, Some extensions of Enström-Kakeya Theorem, Glasnik Mate., 31(1996), 239-244.