Abstract
In this article, we count the number of distinct real roots of certain polynomials in terms of Bezoutian form. As an application, we construct certain irreducible polynomials over the rational number field which have given number of real roots and by the result of Oz Ben-Shimol [On Galois groups of prime degree polynomials with complex roots, Algebra Disc. Math. 2 (2009), pp. 99–107], we obtain an algorithm to construct irreducible polynomials of prime degree p whose Galois groups are isomorphic to S p or A p .
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.