KnowraPolynomial rootPolynomial rootA polynomial root is a value at which the polynomial evaluates to zero. It is also called a zero of the polynomial.BriefConnectFactor theorem: A theorem stating that a polynomial has root a exactly when it is divisible by x − a. It turns the condition that a value is a root into a factorization test.Polynomial: An expression formed from constants and variable powers with nonnegative integer exponents. A root is defined by evaluating this expression and obtaining zero.Root-finding algorithm: A procedure for approximating or determining values where a function equals zero. Polynomial roots are the targets of both exact and numerical root-finding.Complex root: A complex number at which a polynomial with complex coefficients evaluates to zero. Complex roots include nonreal solutions that a real graph cannot display as axis crossings.Fundamental theorem of algebra: Every nonconstant polynomial with complex coefficients has a complex root, and therefore factors into linear terms over the complex numbers. It guarantees the total number of roots when multiplicity is counted.Polynomial equation: An equation that sets a polynomial expression equal to another expression, often zero. Solving a polynomial equation means finding values that make its polynomial side zero.Rational root theorem: A theorem restricting the possible rational roots of a polynomial with integer coefficients. It narrows the candidates when searching for rational polynomial roots.Real root: A real number at which a polynomial evaluates to zero. Real roots are only the real-valued subset of all possible polynomial roots.Multiplicity of a root: The number of times the corresponding linear factor occurs in a polynomial’s factorization. Multiplicity distinguishes repeated roots from roots that occur once.Zero of a function: An input at which a function’s output is zero. A polynomial root is the function-zero idea applied to a polynomial.Show all 21Linked from 17 pagesIntermediate 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.Descartes' rule of signsNarrower topic: The rule bounds how many polynomial roots lie on each side of zero.Bolzano's theoremBroader topic: For real polynomials, endpoint sign changes certify a real root between the endpoints.Abel–Ruffini theoremRelated: The theorem concerns whether all roots can be expressed through a fixed radical formula.Show all 17