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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- Dec 1st 2010, 08:30 AMdougN-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! - Dec 1st 2010, 02:06 PMDrexel28
- Dec 1st 2010, 07:17 PMtopspin1617
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 $\displaystyle f(x)$ has an n-fold root if and only if $\displaystyle f^{\prime}(x)$ has an (n-1)-fold root, and using induction.