Counting the number of distinct real roots of certain polynomials by Bezoutian and the Galois groups over the rational number field

DOI10.1080/03081087.2012.689983zbMath1285.12001OpenAlexW2003654581MaRDI QIDQ5300033

Shuichi Otake

Publication date: 24 June 2013

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2012.689983

zbMATH Keywords

Galois groupBezoutianirreducible polynomialsnumber of real roots

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10)

Related Items (2)

Some remarks on the non-real roots of polynomials ⋮ On the discriminant of certain quadrinomials

Cites Work

• The Galois groups of the polynomials \(X^ n+aX\ell +b\)
• The Galois groups of the polynomials \(x^ n+ax^ s+b\). II
• The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations

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