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

    Fundamental Theorem of Algebra

    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