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Polynomials with Real Roots

Published online by Cambridge University Press:  20 November 2018

J. D. Dixon
J. D. Dixon*
Affiliation:
California Institute of Technology
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Extract

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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