Abstract
It is well known that classic theorems of Markov and Lukach for real polynomials which have a constant sign on a segment are ineffective. In this paper we obtain criteria for the constant sign property on a segment for real polynomials of the fourth degree and formulate certain their generalizations. The mentioned criteria are stated in terms of the coefficients of the polynomials under consideration.
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Original Russian Text © V.E. Geit and N.Zh. Geit, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 11, pp. 80–85.
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Geit, V.E., Geit, N.Z. Criteria for the constant sign property for real polynomials on a segment. Russ Math. 52, 70–75 (2008). https://doi.org/10.3103/S1066369X0811008X
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DOI: https://doi.org/10.3103/S1066369X0811008X