Fundamental theorem of algebra

Math

Definition

The theorem states that every non-constant polynomial of degree n with complex coefficients has exactly n roots (counting multiplicity) in the complex number system. This guarantees that polynomial equations always have solutions.

Examples

  • x² + 1 = 0 has two complex roots: i and −i
  • A cubic polynomial like x³ − 1 has exactly 3 roots
  • x⁴ − 16 = 0 has 4 roots: 2, −2, 2i, −2i
Key Fact

A polynomial of degree n has exactly n roots in the complex numbers (counting multiplicity).

Related Terms

Complex numbers Zeros and multiplicity Polynomial operations Discriminant

Study This Concept

Practice fundamental theorem of algebra with free review games in these units:

Algebra 2 Unit 4: Polynomial Functions