KnowraPolynomial rootLinked fromLinked fromThe 17 pages that link to Polynomial root, each with the reason it gives.All 17Broader topic 4Related 10Narrower topic 3Fundamental theorem of algebraRelated: The theorem guarantees at least one such value in the complex plane.Intermediate value theoremBroader topic: A sign change across an interval guarantees a real polynomial root when the polynomial is continuous.Polynomial factorizationRelated: Each root yields a linear factor over a field containing that value.Discriminant (polynomial)Narrower topic: The discriminant’s vanishing records a collision among the polynomial’s roots.Argument principleBroader topic: Choosing contours around regions of the plane lets the principle count roots there.Vieta's formulasRelated: The roots are the quantities whose sums and products appear in the identities.Factor theoremRelated: A root a is precisely the condition that makes x − a a factor.Abel–Ruffini theoremRelated: The theorem concerns whether all roots can be expressed through a fixed radical formula.Synthetic divisionRelated: The procedure uses the root c corresponding to the divisor x − c.Descartes' rule of signsNarrower topic: The rule bounds how many polynomial roots lie on each side of zero.Newton's identitiesRelated: The identities recover information about roots from their symmetric sums.Polynomial remainder theoremRelated: A candidate root a is verified by checking that the remainder p(a) is zero.Gauss–Lucas theoremNarrower topic: The theorem’s geometric region is built from the locations of these zeros.Nth rootRelated: An nth root of a is a polynomial root of xⁿ − a, though the phrase has broader uses.Bolzano's theoremBroader topic: For real polynomials, endpoint sign changes certify a real root between the endpoints.Cubic functionRelated: Roots determine where a cubic function crosses or touches the x-axis.Schinzel's theoremBroader topic: The theorem asserts that reduced polynomials have roots for infinitely many prime moduli.
KnowraPolynomial rootLinked fromLinked fromThe 17 pages that link to Polynomial root, each with the reason it gives.All 17Broader topic 4Related 10Narrower topic 3Fundamental theorem of algebraRelated: The theorem guarantees at least one such value in the complex plane.Intermediate value theoremBroader topic: A sign change across an interval guarantees a real polynomial root when the polynomial is continuous.Polynomial factorizationRelated: Each root yields a linear factor over a field containing that value.Discriminant (polynomial)Narrower topic: The discriminant’s vanishing records a collision among the polynomial’s roots.Argument principleBroader topic: Choosing contours around regions of the plane lets the principle count roots there.Vieta's formulasRelated: The roots are the quantities whose sums and products appear in the identities.Factor theoremRelated: A root a is precisely the condition that makes x − a a factor.Abel–Ruffini theoremRelated: The theorem concerns whether all roots can be expressed through a fixed radical formula.Synthetic divisionRelated: The procedure uses the root c corresponding to the divisor x − c.Descartes' rule of signsNarrower topic: The rule bounds how many polynomial roots lie on each side of zero.Newton's identitiesRelated: The identities recover information about roots from their symmetric sums.Polynomial remainder theoremRelated: A candidate root a is verified by checking that the remainder p(a) is zero.Gauss–Lucas theoremNarrower topic: The theorem’s geometric region is built from the locations of these zeros.Nth rootRelated: An nth root of a is a polynomial root of xⁿ − a, though the phrase has broader uses.Bolzano's theoremBroader topic: For real polynomials, endpoint sign changes certify a real root between the endpoints.Cubic functionRelated: Roots determine where a cubic function crosses or touches the x-axis.Schinzel's theoremBroader topic: The theorem asserts that reduced polynomials have roots for infinitely many prime moduli.