Relationship between the zeros of two polynomials

Citations of this article
Mendeley users who have this article in their library.
Get full text


In this paper, we shall follow a companion matrix approach to study the relationship between zeros of a wide range of pairs of complex polynomials, for example, a polynomial and its polar derivative or Sz.-Nagy's generalized derivative. We shall introduce some new companion matrices and obtain a generalization of the Weinstein-Aronszajn Formula which will then be used to prove some inequalities similar to Sendov conjecture and Schoenberg conjecture and to study the distribution of equilibrium points of logarithmic potentials for finitely many discrete charges. Our method can also be used to produce, in an easy and systematic way, a lot of identities relating the sums of powers of zeros of a polynomial to that of the other polynomial. © 2009 Elsevier Inc.




Cheung, W. S., & Ng, T. W. (2010). Relationship between the zeros of two polynomials. Linear Algebra and Its Applications, 432(1), 107–115.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free