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Math Help - N-fold root of a polynomial

  1. #1
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    N-fold root of a polynomial

    Let be f a real polynomial that is the sum of n monomials. Prove that there is no nonzero, at least n-fold root of the polynomial.

    Any help would be appreciated!
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by doug View Post
    Let be f a real polynomial that is the sum of n monomials. Prove that there is no nonzero, at least n-fold root of the polynomial.

    Any help would be appreciated!
    What does N-fold mean? I assume this is multivariable polynomials, right?
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  3. #3
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    I think it just means a root of multiplicity n.

    Start by assuming the polynomial has a nonzero constant term (note that in proving this statement, we may ignore any common factors the monomials have; see if you can understand why).

    Then try to prove that f(x) has an n-fold root if and only if f^{\prime}(x) has an (n-1)-fold root, and using induction.
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