•  
  •  
 

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

© Copyright 1951 by the Iowa Academy of Science, Inc.

Language

EN

File Format

application/pdf

Share

COinS
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.