Home > Iowa Academy of Science > Proceedings of the Iowa Academy of Science > Volume 58 (1951) > Annual Issue

#### Article Title

#### Document Type

Research

#### Abstract

A simple method of finding limits for the absolute values of the zeros of polynomials will be given in this paper. The radius of a circle about the origin in the complex plane will be found from the coefficient of the polynomial such that all the zeros will lie on or within this circle. For certain polynomials a second circle will be found such that the zeros will lie on or outside this circle. In finding these circles the following well-known theorem of Rouché is used. Rouché's Theorem is very useful. By means of it the fundamental theorem of algebra and other important results may be established. The proof of Rouché's Theorem is ordinarily based on residue theory and may be found in most books on the theory of functions of a complex variable. Rouché, however, used series expansions to prove his theorem.

#### Publication Date

1951

#### Journal Title

Proceedings of the Iowa Academy of Science

#### Volume

58

#### Issue

1

#### First Page

311

#### Last Page

312

#### Copyright

©1951 Iowa Academy of Science, Inc.

#### Language

en

#### File Format

application/pdf

#### Recommended Citation

Stoner, Wm. J.
(1951)
"Theorem on the Zeros of Polynomials,"
*Proceedings of the Iowa Academy of Science, 58(1),* 311-312.

Available at:
https://scholarworks.uni.edu/pias/vol58/iss1/37