1. 1/27/20169-7 9-7 Fundamental Theorem of Algebra

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

3. 1/27/20169-7 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

4. 1/27/20169-7 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 = 3 + 2 + 1 = 6 How many x-intercepts does f(x) have? 3

5. 1/27/20169-7 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)

6. Application… Find all zeros and their multiplicities of: 1/27/20169-7

7. Application…. Let a)Verify that -3i is a zero b)Find the remaining zeros of p(x) and their multiplicities. 1/27/20169-7

8. Application Find all zeros of