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Documentation / Mathematica / Built-in Functions / Algebraic Computation / Equation Solving /

Root

FilledSmallSquare Root[f, k] represents the k root of the polynomial equation f[x] == 0.

FilledSmallSquare f must be a Function object such as (#^5 - 2 # + 1)&.

FilledSmallSquare Root[f, k] is automatically reduced so that f has the smallest possible degree and smallest integer coefficients.

FilledSmallSquare The ordering used by Root takes real roots to come before complex ones, and takes complex conjugate pairs of roots to be adjacent.

FilledSmallSquare The coefficients in the polynomial f[x] can involve symbolic parameters.

FilledSmallSquare For linear and quadratic polynomials f[x], Root[f, k] is automatically reduced to explicit rational or radical form.

FilledSmallSquare N finds the approximate numerical value of a Root object.

FilledSmallSquare Operations such as Abs, Re, Round and Less can be used on Root objects.

FilledSmallSquare Root[f, k] is treated as a numeric quantity if f contains no symbolic parameters.

FilledSmallSquare Root by default isolates the roots of a polynomial using approximate numerical methods. No cases are known where this approach fails. SetOptions[Root, ExactRootIsolation->True] will however make Root use much slower but fully rigorous methods.

FilledSmallSquare See Section 1.5.7 and Section 3.4.2.

FilledSmallSquare See also: Solve, RootReduce, ToRadicals, RootSum, Extension, Algebraics.

FilledSmallSquare Related package: Algebra`RootIsolation`.

FilledSmallSquare New in Version 3.

Further Examples