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Thread: Multiple root

  1. #1
    Junior Member
    Jun 2011

    Multiple root

    Let P be an arbitrary field, while C is the complex field. f(x) is a polynomial in P with degree >0. Suppose f has no multiple factor in P, prove then f has no multiple root in C.

    Here, we mean by g(x) is a multiple factor of f(x), if g(x) is irreducible, and for some k>1, g^k(x)\mid f(x).
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  2. #2
    MHF Contributor Drexel28's Avatar
    Nov 2009
    Berkeley, California

    Re: Multiple root

    This doesn't make any sense as written? I'm going to assume that P is a subfield of \mathbb{C}. Recall then that f having no multiple roots is equivalent to (f,f')=1, which is trivially independent of what field you are discussing. Once again, this question dreally doesn't make sense.
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