Math
Fundamental theorem of algebra.
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
Real-world.
- 1 x² + 1 = 0 has two complex roots: i and −i
- 2 A cubic polynomial like x³ − 1 has exactly 3 roots
- 3 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).