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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2005 • Question 7

Question

Math 6310 • Algebra Fall 2005 • Question 7

Let \(\alpha \) be a primitive fifth root of 1 and \(f(x)=x^5+5x^2+4\). Show that \(f(x)\) is irreducible in \(\mathbb {Q}[\alpha ]\).

Raw LaTeX

Let \(\alpha\) be a primitive fifth root of 1 and \(f(x)=x^5+5x^2+4\).
Show that \(f(x)\) is irreducible in \(\mathbb{Q}[\alpha]\).

Topic Tags

Irreducible Polynomials