Zero free region & location of zero’s of a polynomial with restricted coefficients

Aijaz Ahmad; Mushtaq. A.Shah; AjayGupta

doi:https://doi.org/10.14445/22315373/IJMTT-V65I10P504

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 10 | Year 2019 | Article Id. IJMTT-V65I10P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I10P504

Zero free region & location of zero’s of a polynomial with restricted coefficients

Aijaz Ahmad, Mushtaq. A.Shah, AjayGupta

Citation :

Aijaz Ahmad, Mushtaq. A.Shah, AjayGupta, "Zero free region & location of zero’s of a polynomial with restricted coefficients," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 10, pp. 27-34, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I10P504

Abstract

Concerning the distribution of a polynomial a famous result is due to Enestrom – Kakeya which states that if P(z) = n∑i=0aizi is an nth degree polynomial, such that an≥an-1≥...≥a1≥a0>0s Then all zero’s of P(z) lie in |z|≤1. In this paper we relax the hypothesis in several ways and obtain a generalization of above result, we also present a result on the zero free region of certain polynomials.

Keywords

zero’s of polynomial, coefficients, bounds, zero free region.

References

[1] N. K Govil and Q. I Rahman, on the Enestrom–Kakeya theorem tohoku Math. J, 20 (1968), 126-136
[2] A. Joyal, G. Labelle and Q. I Rahman, on the location of zeros of polynomials Canadian Math, Bull. 10 (1967), 53-63
[3] M. Mardan Geometry of polynomials,2^nd Ed, Math surveys, No.3 Amer. Math Soc providence, R. I. 1966.