1/27/20169-7 9-7 Fundamental Theorem of Algebra. Intro Find all zeros for each of the following: Multiplicity – When more than one zero occurs at the.

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1/27/ Fundamental Theorem of Algebra

Intro Find all zeros for each of the following: Multiplicity – When more than one zero occurs at the same spot

1/27/ Fundamental Theorem of Algebra Number of Zeros of a Polynomial Theorem: A polynomial of degree n > 1 has exactly n complex zeros, if multiplicities are counted. Theorem - A polynomial of degree n has at most n real zeros

1/27/ Multiplicity and Degree What are the zeros of f(x)? x = -1/2; 3; 3/4 Which zero has a mulitplicty of 3 x = -1/2 What is the degree of f(x)? deg = = 6 How many x-intercepts does f(x) have? 3

1/27/ Conjugate Zeros Theorem Conjugate Zeros Theorem: If a + bi is a zero of of p(x) then a – bi is also a zero of p(x)

Application… Find all zeros and their multiplicities of: 1/27/

Application…. Let a)Verify that -3i is a zero b)Find the remaining zeros of p(x) and their multiplicities. 1/27/

Application Find all zeros of