MathLiveFundamental theorem of algebra
Every non-constant polynomial with complex coefficients has at least one complex root. It guarantees that the complex numbers are algebraically closed and is used to justify factoring polynomials into linear factors.
\forall P \in \mathbb{C}[X]\setminus \mathbb{C},\ \exists x \in \mathbb{C},\ P(x) = 0What the symbols mean
| a polynomial with complex coefficients, in the indeterminate X | |
| the field of complex numbers | |
| a complex number that is a root of P |
About this formula
- FieldMathematics
- TopicAlgebra
- LevelUniversity
- Also calledd'Alembert's theorem, every polynomial has a complex root, non-constant polynomial has a root, complex polynomial root existence, algebraically closed complex numbers
- SourceWikidata Q192760
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