On the Location of Zeros of Polynomials

1967 ◽  
Vol 10 (1) ◽  
pp. 53-63 ◽  
Author(s):  
A. Joyal ◽  
G. Labelle ◽  
Q.I. Rahman
Keyword(s):  
Classical Result ◽  
Zeros Of Polynomials ◽  
Location Of Zeros

The different results proved in this paper do not have very much in common. Since they all deal with the location of the zeros of a polynomial, we have decided to put them in one place. Improving upon a classical result of Cauchy we obtain in § 2 a circle containing all the zeros of a polynomial. In § 3 we obtain an extension of the well known theorem of Enestrőm and Kakeya concerning the zeros of a polynomial whose coefficients are non-negative and monotonie.

The location of critical points of polynomials

2019 ◽  
Vol 12 (07) ◽  
pp. 1950087
Author(s):  
Suhail Gulzar ◽  
N. A. Rather ◽  
F. A. Bhat
Keyword(s):  
Complex Plane ◽  
Simple Proof ◽  
Critical Points ◽  
Classical Result ◽  
Zeros Of Polynomials ◽  
Linear Combinations ◽  
Incomplete Polynomials ◽  
Location Of Zeros ◽  
Set Of Points

Given a set of points in the complex plane, an incomplete polynomial is defined as one which has these points as zeros except one of them. Recently, the classical result known as Gauss–Lucas theorem on the location of zeros of polynomials and their derivatives was extended to the linear combinations of incomplete polynomials. In this paper, a simple proof of this result is given, and some results concerning the critical points of polynomials due to Jensen and others have extended the linear combinations of incomplete polynomials.

scholarly journals On the regions containing all the zeros of polynomials and related analytic functions

2021 ◽  
Vol 8 (2) ◽  
pp. 331-337
Author(s):  
Nisar Ahmad Rather ◽  
◽  
Ishfaq Dar ◽  
Aaqib Iqbal ◽  
◽  
...  
Keyword(s):  
Analytic Functions ◽  
Zeros Of Polynomials ◽  
Location Of Zeros ◽  
Standard Techniques

In this paper, by using standard techniques we shall obtain results with relaxed hypothesis which give zero bounds for the larger class of polynomials. Our results not only generalizes several well-known results but also provide better information about the location of zeros. We also obtain a similar result for analytic functions. In addition to this, we show by examples that our result gives better information on the zero bounds of polynomials than some known results.

On the Location of Zeros of Polynomials

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Prasanna Kumar ◽  
Ritu Dhankhar
Keyword(s):  
Zeros Of Polynomials ◽  
Location Of Zeros

scholarly journals Location of zeros of polynomials

2009 ◽  
Vol 50 (1-2) ◽  
pp. 306-313 ◽  
Author(s):  
Chadia Affane-Aji ◽  
Neha Agarwal ◽  
N.K. Govil
Keyword(s):  
Zeros Of Polynomials ◽  
Location Of Zeros

scholarly journals Number of zeros of a polynomial in a given domain

2011 ◽  
Vol 42 (4) ◽  
pp. 531-536
Author(s):  
A. Ebadian ◽  
M. Bidkhamandm ◽  
Eshaghi Gordji
Keyword(s):  
Numerical Methods ◽  
Approximation Theory ◽  
Zeros Of Polynomials ◽  
Number Of Zeros ◽  
Location Of Zeros

In this paper, we obtain results concerning the bound for the number of zeros for the polynomial $p(z)$ which generalize earlier well-known result due to Bidkham and Dewan [{\it On the zeros of a polynomial}, Numerical Methods and Approximation Theory III, Ni\v{s} (1987), 121--128] and Mohammad [{\it On the zeros of polynomials}, Amer. Math. Monthly, 72 (1965), 631-633]. We also obtain result for location of zeros of polynomial $p(z)=\sum\limits_{i=0}^m \frac{a_i}{(i!)^\lambda} z^i+a_nz^n$, $a_n\neq 0$, $0\leq m\leq n-1$, $\lambda\geq 0$.\

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