About: Complex conjugate root theorem

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In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P. It follows from this (and the fundamental theorem of algebra) that, if the degree of a real polynomial is odd, it must have at least one real root. That fact can also be proven by using the intermediate value theorem.

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rdfs:label	Complex conjugate root theorem (en)
rdfs:comment	In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P. It follows from this (and the fundamental theorem of algebra) that, if the degree of a real polynomial is odd, it must have at least one real root. That fact can also be proven by using the intermediate value theorem. (en)
sameAs	Complex conjugate root theorem Complex conjugate root theorem
dbp:wikiPageUsesTemplate	dbt:Math dbt:Reflist dbt:Short_description
Subject	Articles containing proofs Theorems in complex analysis Theorems about polynomials
gold:hypernym	Polynomial
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Complex_conjugate_root_theorem?oldid=1027858118&ns=0
Wikipage page ID	9178245 (xsd:integer)
page length (characters) of wiki page	5187 (xsd:nonNegativeInteger)
Wikipage revision ID	1027858118 (xsd:integer)
Link from a Wikipage to another Wikipage	Articles containing proofs Theorems in complex analysis Lemma (mathematics) Zero of a function Coefficient Complex conjugate Eigenvalues and eigenvectors Orthogonal matrix Fundamental theorem of algebra Intermediate value theorem Irreducible polynomial Mathematics Matrix (mathematics) Multiplicity (mathematics) Polynomial Real number Theorems about polynomials
has abstract	In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P. It follows from this (and the fundamental theorem of algebra) that, if the degree of a real polynomial is odd, it must have at least one real root. That fact can also be proven by using the intermediate value theorem. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Complex_conjugate_root_theorem
is Link from a Wikipage to another Wikipage of	Geometrical properties of polynomial roots Line spectral pairs List of polynomial topics Complex conjugate
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Complex_conjugate_root_theorem

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