Fundamental theorem of algebra

GPTKB entity

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 mathematics theorems in complex analysis
gptkbp:field	gptkb:algebra complex analysis
gptkbp:first_proved_by	gptkb:Carl_Friedrich_Gauss
https://www.w3.org/2000/01/rdf-schema#label	Fundamental theorem of algebra
gptkbp:implies	degree n polynomial has n roots in complex numbers (counting multiplicities)
gptkbp:importantFor	establishes algebraic closure of complex numbers
gptkbp:influenced	complex analysis field theory development of modern algebra
gptkbp:languageOfName	English
gptkbp:notable_proof_by	gptkb:Augustin-Louis_Cauchy gptkb:Carl_Friedrich_Gauss gptkb:Jean-Robert_Argand gptkb:Jean_le_Rond_d'Alembert gptkb:Niels_Henrik_Abel
gptkbp:originalLanguage	gptkb:Latin
gptkbp:provenBy	gptkb:algebra gptkb:topology gptkb:Galois_theory complex analysis real analysis
gptkbp:relatedTo	gptkb:complex_plane field theory roots of polynomials algebraic closure of complex numbers
gptkbp:state	every non-constant single-variable polynomial with complex coefficients has at least one complex root
gptkbp:year_of_first_proof	1799
gptkbp:bfsParent	gptkb:Bézout's_theorem gptkb:Wilhelm_Gauss gptkb:Louis_Gauss gptkb:Louis_Gauß gptkb:Wilhelm_Gauß
gptkbp:bfsLayer	6