Geodesic
Criteria for the constant sign property for real polynomials on a segment
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2008), pp. 80-85.

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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 generalizations of them. The mentioned criteria are stated in terms of the coefficients of the polynomials under consideration.
Keywords: nonnegative, nonpositive polynomials, polynomials with the least deviation from zero in the integral metric. 
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V. È. Gheit; N. Zh. Gheit. Criteria for the constant sign property for real polynomials on a segment. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2008), pp. 80-85. http://geodesic.mathdoc.fr/item/IVM_2008_11_a7/

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