#### Document Type

Article

#### Publication Date

1-2003

#### Abstract

Given a polynomial *p* of degree *n *≥ 2 and with at least two distinct roots let *Z(p)* = { *z*: *p(z) *= 0}. For a fixed root α ∈* Z(p)* we define the quantities *ω(p, α)* := min (formula) and (formula). We also define *ω (p)* and *τ (p)* to be the corresponding minima of *ω (p,α)* and τ* (p,α)* as α runs over *Z(p)*. Our main results show that the ratios *τ (p,α)/ω (p,α)* and *τ (p)/ω (p)* are bounded above and below by constants that only depend on the degree of *p*. In particular, we prove that (formula), for any polynomial of degree *n*.

#### Publication Title

Proceedings of the American Mathematical Society

#### Volume

131

#### Issue

1

#### First Page

253

#### Last Page

264

#### Required Publisher's Statement

First published in "Proceedings of the American Mathematical Society" in 2003, published by the American Mathematical Society.

#### Recommended Citation

Ćurgus, Branko and Mascioni, Vania, "On the Location of Critical Points of Polynomials" (2003). *Mathematics*. 7.

http://cedar.wwu.edu/math_facpubs/7

## Comments

Communicated by N. Tomczak-Jaegermann