Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-12-01T03:58:15.737Z Has data issue: false hasContentIssue false
  • English
  • Français

Polynomials with Real Roots

Published online by Cambridge University Press:  20 November 2018

J. D. Dixon
J. D. Dixon*
Affiliation:
California Institute of Technology
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In a recent issue of this Bulletin a problem equivalent to the following is proposed by Moser and Pounder [1]:

If ax2+bx+c is a polynomial with real coefficients and real roots then a+b+c ≤9/4 max (a, b, c).

The object of this note is to prove the following theorems which generalise this result.

Theorem 1. Let αn be the smallest constant such that n for all polynomials

1

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 5 , Issue 3 , September 1962 , pp. 259 - 263
Copyright
Copyright © Canadian Mathematical Society 1962

References

1. Moser, L. and Pounder, J.R., Problem 53, Canadian Mathematical Bulletin, vol. 5 (1962) 70.Google Scholar
2. Hardy, , Littlewood and Polya, Inequalities, Cambridge University Press (1952).Google Scholar