Location of the Zeros of a Polynomial with Positive Ordered Coefficients

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows the location of the zeros of a polynomial of degree seven with positive coefficients. When the coefficients are ordered , the Eneström–Kakeya theorem states that the zeros (red points) lie in the unit circle, represented by the black circle centered in the origin. Furthermore, regardless of the order of the coefficients, the zeros lie in the ring , where and , represented by the blue circles centered in the origin.

[more]

The ring area is bigger than the unit circle area, so the inner circle and the unit circle give a better ring than using the outer circle.

[less]

Contributed by: Vanessa Botta and Evanize Rodrigues Castro (June 2013)
(supported by FAPESP - Grant 2012/08248-9)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Reference

[1] G. V. Milovanovic, D. S. Mitrinovic, and Th. M. Rassias, Topics in Polynomials: Extremal Problems, Inequalities, Zeros, Singapore: World Scientific, 1994.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send