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

1 Answer
Topscooter
Jan 6, 2016

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.

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