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:field |
gptkb:algebra
complex analysis |
| gptkbp:hasProofsOf |
gptkb:algebra
gptkb:topology complex analysis real analysis |
| 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 that the field of complex numbers is algebraically closed
|
| gptkbp:namedAfter |
gptkb:algebra
|
| 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:d'Alembert–Gauss_theorem
|
| gptkbp:bfsLayer |
7
|