The Fundamental Theorem of Algebra

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Presentation transcript:

The Fundamental Theorem of Algebra

Example

Roots and Zeros Friedrich Gauss

Example

Example

Example

Complex Conjugate Root Theorem

Example

Example

Example

Example

Example

Example

Roots and Zeros

Roots and Zeros 2 6 4 Number of Positive Real Zeros Number of Negative Real Zeros Number of Imaginary Zeros Total 2 6 4 Roots and Zeros

So, the number of imaginary zeros for all polynomial functions must be an even number Roots and Zeros

Roots and Zeros

Roots and Zeros

Roots and Zeros

Roots and Zeros Roots and Zeros

Roots and Zeros

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

3 Practice Problems

Practice Problems

Practice Problems

Page 449 - 451 20 – 22, 26 – 36 even, 74, 75 Homework