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nietzsche
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Homework Statement
Prove that if f is a polynomial function of degree n, then f has at most n roots, i.e., there are at most n numbers a with f(a) = 0.
Homework Equations
N/A
The Attempt at a Solution
I know that I'm supposed to use induction on the degree of the polynomial. If we assume a polynomial of degree 0, then f(x) is a constant and has no real roots.
Now I don't know how to use induction on that statement. It's very easy to know intuitively but I'm having a lot of trouble formalizing this into a proof. Any hints would be greatly appreciated.
By the way, another question: what if f(x) = 0? How many roots does that have?
Thanks.