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Title: Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5
Authors: Kostov, Vladimir
Keywords: Hyperbolic Polynomial
Hyperbolicity Domain
Overdetermined Stratum
Issue Date: 2002
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 28, No 2, (2002), 117p-152p
Abstract: A real polynomial of one real variable is hyperbolic (resp. strictly hyperbolic) if it has only real roots (resp. if its roots are real and distinct). We prove that there are 116 possible non-degenerate configurations between the roots of a degree 5 strictly hyperbolic polynomial and of its derivatives (i.e. configurations without equalities between roots). The standard Rolle theorem allows 286 such configurations. To obtain the result we study the hyperbolicity domain of the family P (x; a, b, c) = x^5 − x^3 + ax^2 + bx + c (i.e. the set of values of a, b, c ∈ R for which the polynomial is hyperbolic) and its stratification defined by the discriminant sets Res(P^(i) , P^(j) ) = 0, 0 ≤ i < j ≤ 4.
Description: ∗ Research partially supported by INTAS grant 97-1644
ISSN: 1310-6600
Appears in Collections:Volume 28 Number 2

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