Lesson 2.5 The Fundamental Theorem of Algebra

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Presentation transcript:

Lesson 2.5 The Fundamental Theorem of Algebra

For f(x) where n > 0, there is at least one zero in the complex number system Complex → real and imaginary Real zeros → can see on graph Imaginary → cannot see on graph f(x) of degree n will have exactly n zeros (real and imaginary) Complex zeros always occur in conjugate pairs “If a + bi is a zero, then a – bi is also”

How do we find the zeros of For a polynomial f(x) with degree n: Find real zero(s) using calculator or Factor Theorem and Synthetic Division If there are n real roots, stop Divide out real zeros to obtain a 2nd degree equation Solve 2nd degree equation for x (use Quadratic Equation if necessary)

Linear Factorization

Example 1

Example 2

HW 2-5 pg 234: 1-11 odd, 17-20, 21-29 odd, 35, 37