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
- 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