The Fundamental Theorem of Algebra
GPTKB entity
Statements (43)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
|
| gptkbp:applies_to |
polynomial equations
|
| gptkbp:can_be_expressed_in_terms_of |
roots of unity
|
| gptkbp:consequences |
the topology of the complex plane
|
| gptkbp:has_implications_for |
numerical methods
|
| https://www.w3.org/2000/01/rdf-schema#label |
The Fundamental Theorem of Algebra
|
| gptkbp:illustrated_by |
examples of quadratic equations
|
| gptkbp:is_a_basis_for |
further studies in mathematics
|
| gptkbp:is_a_critical_concept_in |
the study of functions
|
| gptkbp:is_a_foundation_for |
modern algebra
the field of algebraic geometry |
| gptkbp:is_a_result_that_connects |
algebra and analysis
|
| gptkbp:is_a_subject_of |
abstract algebra
mathematical research |
| gptkbp:is_a_theorem_that_can_be_generalized_to |
higher dimensions.
|
| gptkbp:is_a_theorem_that_has |
gptkb:historical_significance
practical applications in engineering |
| gptkbp:is_applicable_to |
real coefficients polynomials
|
| gptkbp:is_cited_in |
mathematical proofs
|
| gptkbp:is_connected_to |
gptkb:quantum_field_theory
|
| gptkbp:is_discussed_in |
mathematical literature
|
| gptkbp:is_essential_for |
complex numbers
solving polynomial equations the behavior of polynomials |
| gptkbp:is_explored_in |
advanced mathematics courses
|
| gptkbp:is_fundamental_to |
gptkb:Mathematics
|
| gptkbp:is_often_associated_with |
the work of mathematicians throughout history
|
| gptkbp:is_often_described_as |
Algebra's Fundamental Theorem
|
| gptkbp:is_related_to |
complex analysis
the concept of continuity the degree of a polynomial |
| gptkbp:is_significant_for |
the study of polynomial functions
|
| gptkbp:is_taught_in |
undergraduate mathematics courses
|
| gptkbp:is_used_in |
gptkb:Mathematics
|
| gptkbp:is_used_in_proofs_of |
other mathematical theorems
|
| gptkbp:key |
the theory of equations
|
| gptkbp:key_concept |
mathematical analysis
|
| gptkbp:state |
Every non-constant polynomial equation has at least one complex root.
|
| gptkbp:topics |
mathematical education
|
| gptkbp:was_a_result_of |
the interplay between algebra and geometry
|
| gptkbp:was_proven_by |
gptkb:Carl_Friedrich_Gauss
|
| gptkbp:bfsParent |
gptkb:Carl_Friedrich_Gauss
|
| gptkbp:bfsLayer |
4
|