Question

What is the relationship between the degree of a polynomial and the maximum numbers of zeros it can have?

Answer 1

The fundamental theorem of algebra gives us the relationship.

Explanation:

This theorem tells us that any polynomial `P in CC[X]` has EXACTLY `n` roots in `CC` (each one of them is different or not), if `n = deg(P)`.

This means that you can write `P` as the product of simple polynomials in `CC` : `P(X) = (X - a_1)^(alpha_1)(X - a_2)^(alpha_2)...(X - a_n)^(alpha_n)` with `a_i` defined such that `P(a_i) = 0` and `sum_(i=1)^nalpha_i = n = deg(P)`.

I hope it answers your question.