This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


Root[f, k]
represents the k^(th) root of the polynomial equation f[x]0.
Root[poly, x, k]
gives the k^(th) root of the polynomial poly in x.
  • f must be a Function object such as (#^5-2#+1)&.
  • Root[f, k] is automatically reduced so that f has the smallest possible degree and smallest integer coefficients.
  • The ordering used by Root takes real roots to come before complex ones, and takes complex conjugate pairs of roots to be adjacent.
  • The coefficients in the polynomial f[x] can involve symbolic parameters.
  • For linear and quadratic polynomials f[x], Root[f, k] is automatically reduced to explicit rational or radical form.
  • For other polynomials, ToRadicals can be used to convert to explicit radicals.
  • N finds the approximate numerical value of a Root object.
  • Root[f, k] is treated as a numeric quantity if f contains no symbolic parameters.
  • Root by default isolates the complex roots of a polynomial using validated numerical methods. SetOptions[Root, ExactRootIsolation->True] will make Root use symbolic methods that are usually much slower.
New in 3