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!
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.