Let F be a field and let f(x) be anirreducible polynomial in F[x]. Thenf (x) has a multiple root in somefield extension if and only iff'(x) = 0.

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 8E: Let be an irreducible polynomial over a field . Prove that is irreducible over for all nonzero ...

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Let F be a field and let f(x) be an irreducible polynomial in F[x]. Then f (x) has a multiple root in some field extension if and only if f'(x) = 0.