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.
Citation
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
