%0 Journal Article
%T Infinite Parametric Families of Irreducible Polynomials with a Prescribed Number of Complex Roots
%A Catalin Nitica
%A Viorel Nitica
%J Open Journal of Discrete Mathematics
%P 1-6
%@ 2161-7643
%D 2019
%I Scientific Research Publishing
%R 10.4236/ojdm.2019.91001
%X In this note, for any pair of natural numbers (n,k), n≥3, k≥1, and 2k<n, we construct an infinite family of irreducible polynomials of degree n, with integer
coefficients, that has exactly n-2k complex non-real roots
if n is even and has exactly n-2k-1 complex non-real roots
if n is odd. Our work generalizes a
technical result of R. Bauer, presented in the classical monograph ¡°Basic
Algebra¡± of N. Jacobson. It is used there to construct polynomials with Galois
groups, the symmetric group. Bauer¡¯s result covers the case k=1 and n odd prime.
%K &
%K #205
%K rreducible Polynomial
%K Complex Roots
%K Real Roots
%K Galois Theory
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=89182