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The zeros of a certain family of trinomials

Published online by Cambridge University Press:  18 May 2009

Karl Dilcher ,
James D. Nulton  and
Kenneth B. Stolarsky
Karl Dilcher
Affiliation:
Dept. of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, CanadaB3H 3J5
James D. Nulton
Affiliation:
2045 Montclair Street, San Diego, California 92104, U.S.A.
Kenneth B. Stolarsky
Affiliation:
Dept. of Mathematics, 1409 West Green, University of Illinois, Urbana, Illinois 61801, U.S.A.
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Many of the classical inequalities of analysis can be written in the form P(x) ≥ 0 for x ∈ I or P(x) > 0 for x ∈ I′, where P(x) is a polynomial and I′ ⊂ I are certain intervals on the real line. This gives rise to the question of where the zeros of P(x) are located. For example, if f is a polynomial with real zeros, then an inequality of Laguerre [8, p. 171 f.] asserts that

for all x. A detailed study of the zeros of this particular P(x) has been made [5].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 1 , January 1992 , pp. 55 - 74
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

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