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February 2007 Reducibility and the Galois Group of a Parametric Family of Quintic Polynomials
Melisa J. Lavallee, Blair K. Spearman, Kenneth S. Williams
Missouri J. Math. Sci. 19(1): 2-10 (February 2007). DOI: 10.35834/mjms/1316092231

Abstract

It is shown that $f_{t}(x)=x^{5}+(t^{2}-3125)x-4(t^{2}-3125)$ ($t \in \mathbb{Q}$) is reducible in $\mathbb{Q} [x]$ if and only if $t=0$. When $t \neq 0$ it is shown that $\text{Gal} (f_{t}) \simeq D_{5}$ or $A_{5}$, and necessary and sufficient conditions are given for each possibility.

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Melisa J. Lavallee. Blair K. Spearman. Kenneth S. Williams. "Reducibility and the Galois Group of a Parametric Family of Quintic Polynomials." Missouri J. Math. Sci. 19 (1) 2 - 10, February 2007. https://doi.org/10.35834/mjms/1316092231

Information

Published: February 2007
First available in Project Euclid: 15 September 2011

zbMATH: 1142.11073
Digital Object Identifier: 10.35834/mjms/1316092231

Subjects:
Primary: 11R21

Rights: Copyright © 2007 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.19 • No. 1 • February 2007
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