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arXiv · 1703.03313

On realizability of sign patterns by real polynomials

Vladimir Petrov Kostov
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Abstract

The classical Descartes' rule of signs limits the number of positive roots of a real polynomial in one variable by the number of sign changes in the sequence of its coefficients. One can ask the question which pairs of nonnegative integers $(p,n)$, chosen in accordance with this rule and with some other natural conditions, can be the pairs of numbers of positive and negative roots of a real polynomial with prescribed signs of the coefficients. The paper solves this problem for degree $8$ polynomials.

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Vladimir Petrov Kostov. 2017-03-09. On realizability of sign patterns by real polynomials. https://arxiv.org/abs/1703.03313

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