Know the Fundamental Theorem of Algebra

What you'll learn

1. State the Fundamental Theorem of Algebra: every degree-n polynomial has exactly n roots in the complex numbers (counting multiplicity).
2. Demonstrate the theorem for quadratic polynomials by exhaustive case analysis using the discriminant.
3. Explain why the theorem implies every polynomial over the complex numbers factors completely into n linear factors.
4. Explain why real-coefficient polynomials of odd degree must have at least one real root.

Prerequisites

• Solve quadratic equations with complex solutions
• Extend polynomial identities to complex numbers