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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2013 • Question 8

Question

Math 6310 • Algebra Spring 2013 • Question 8

Show that \(f(x)=x^4+4x^2+2\) is irreducible over \(\mathbb {Q}\), and find its Galois group over \(\mathbb {Q}\).

Raw LaTeX

Show that \(f(x)=x^4+4x^2+2\) is irreducible over \(\mathbb{Q}\), and find its Galois group over
\(\mathbb{Q}\).

Topic Tags

Galois Theory Irreducible Polynomials