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Show that the cubic field generated by a root of f(x) = %3D x3 -3x2 - 10x - 8, where f is irreducible over Q, has no power base. Use the fact that disc(f)=(-503)(4).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.4: Zeros Of A Polynomial

Problem 33E: Let where is a field and let . Prove that if is irreducible over , then is irreducible over .

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Question

Show that the cubic field generated by a root of f(x) =
%3D
x3 -3x2 - 10x - 8, where f is irreducible over Q, has no power
base. Use the fact that disc(f)=(-503)(4).

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