Let a and b be nonzero rational numbers. We show that there are an infinite number of essentially different, irreducible, solvable, quintic trinomials X5 + aX + b. On the other hand, we show that there are only five essentially different, irreducible, solvable, quintic trinomials X5+aX2+b, namely, X5 + 5X2 + 3, X5 + 5X2 - 15, X5 + 25X2 + 300, X5 + 100X2 + 1000, and X5 + 250X2 + 625.

Additional Metadata
Keywords Galois group, Irreducible, Quintic trinomials, Solvable
Journal Rocky Mountain Journal of Mathematics
Citation
Spearman, B.K. (Blair K.), & Williams, K.S. (1996). On solvable quintics X5 + aX + b and X5 + aX2 + b. Rocky Mountain Journal of Mathematics, 26(2), 753–772.