Subject:
Mathematics
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Mathematics, Tmm0022
License:
Creative Commons Attribution-NonCommercial 4.0
Language:
English
Media Formats:
Text/HTML

Fundamental Theorem of Algebra

Section 1: Complex Zeros and Fundamental Theorem of Algebra

In this module we will learn about the Fundamental Theorem of Algebra which states that a polynomial of degree n with complex coefficients has at least one complex zero. When this result is applied repeatedly, we get the Complex Factorization Theorem which states that a degree n polynomial has exactly n complex zeros including multiplicity. Thus, we note that a polynomial of degree n can be written as a product of n complex linear factors including multiplicity. We will see that complex zeros occur in conjugate pairs. Further, a degree n polynomial with real coefficients can be written as a product of linear factor and irreducible quadratic factors

Learning Objectives:

  • Complex numbers, magnitude and arithmetic including addition, subtraction, multiplication and division.
  • Apply Complex Factorization Theorem to find all zeros of a polynomial
  • Apply Real Factorization Theorem to find all zeros of a polynomial