Professional paper

Location of roots of polynomials

Mandalena Pranjić
Rajna Rajić orcid.org/0000-0002-0143-5116 ; Rudarsko-geološko-naftni fakultet, Sveučilište u Zagrebu, Zagreb

Abstract

By Rolle's Theorem, any segment whose endpoints are mutually distinct real roots of a polynomial $p:\mathbb{R}\rightarrow\mathbb{R}$ contains at least one stationary point of the polynomial $p.$ Complex analogues of this theorem are presented in this paper: Gauss-Lucas Theorem on the location of stationary points of a polynomial $p:\mathbb{C}\rightarrow\mathbb{C}$ with respect to the roots of the polynomial itself, and Jensen's Theorem on the location of non-real stationary points of a polynomial $p:\mathbb{C}\rightarrow\mathbb{C}$ with real coefficients with respect to its roots. The application of these theorems is illustrated by examples.

Keywords

roots of polynomials; stationary points; derivative

Hrčak ID:

135198

URI

https://hrcak.srce.hr/135198

Publication date:

2.3.2015.

Article data in other languages: croatian

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