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The Discriminant of a Dihedral Quintic Field Defined by a Trinomial X5 + aX + b
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- Journal:
- Canadian Mathematical Bulletin / Volume 45 / Issue 1 / 01 March 2002
- Published online by Cambridge University Press:
- 20 November 2018, pp. 138-153
- Print publication:
- 01 March 2002
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- Article
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Let
${{X}^{5}}\,+\,aX\,+\,b\,\in \,Z\left[ X \right]$ have Galois group 
${{D}_{5}}$. Let 
$\theta $ be a root of 
${{X}^{5}}\,+\,aX\,+\,b$. An explicit formula is given for the discriminant of 
$Q\left( \theta \right)$.
