# Math Help - N-fold root of a polynomial

1. ## 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!

2. Originally Posted by doug
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?

3. 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.