the fundamental theorem of algebra

GPTKB entity

Statements (23)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:alternativeName gptkb:d'Alembert–Gauss_theorem
gptkbp:appliesTo complex numbers
polynomials
gptkbp:category theorems in algebra
theorems in complex analysis
gptkbp:field gptkb:algebra
complex analysis
gptkbp:hasProofsOf gptkb:algebra
gptkb:topology
complex analysis
real analysis
https://www.w3.org/2000/01/rdf-schema#label the fundamental theorem of algebra
gptkbp:implies every polynomial of degree n has exactly n roots in the complex numbers, counting multiplicities
gptkbp:provenBy gptkb:Carl_Friedrich_Gauss
gptkbp:relatedTo gptkb:complex_plane
field theory
algebraic closure
polynomial equation
gptkbp:state every non-constant single-variable polynomial with complex coefficients has at least one complex root
gptkbp:yearProved 1799
gptkbp:bfsParent gptkb:Liouville's_theorem
gptkbp:bfsLayer 6