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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Polynomials with nonnegative coefficients

Authors: R. W. Barnard, W. Dayawansa, K. Pearce and D. Weinberg
Journal: Proc. Amer. Math. Soc. 113 (1991), 77-85
MSC: Primary 30C10
MathSciNet review: 1072329
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Abstract: The authors verify the conjecture that a conjugate pair of zeros can be factored from a polynomial with nonnegative coefficients so that the resulting polynomial still has nonnegative coefficients. The conjecture was originally posed by A. Rigler, S. Trimble, and R. Varga arising out of their work on the Beauzamy-Enflo generalization of Jensen's inequality. The conjecture was also made independently by B. Conroy in connection with his work in number theory. A crucial and interesting lemma is proved which describes general coefficient-root relations for polynomials with nonnegative coefficients and for polynomials for which the case of equality holds in Descarte's Rule of Signs.

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Article copyright: © Copyright 1991 American Mathematical Society

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