This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

Roots

 Rootsyields a disjunction of equations which represent the roots of a polynomial equation.
• You can find numerical values of the roots by applying N.
• Roots can take the following options:
 Cubics True whether to generate explicit solutions for cubics EquatedTo Null expression to which the variable solved for should be equated Modulus 0 integer modulus Multiplicity 1 multiplicity in final list of solutions Quartics True whether to generate explicit solutions for quartics Using True subsidiary equations to be solved
• Roots is generated when Solve and related functions cannot produce explicit solutions. Options are often given in such cases.
• Roots gives several identical equations when roots with multiplicity greater than one occur.
Find roots of univariate polynomial equations:
Find roots of univariate polynomial equations:
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 Scope   (7)
Equation with exact numeric coefficients:
Equation with symbolic coefficients:
General equations of degree five and higher cannot be solved in radicals:
This equation of degree nine is solved in radicals using factorization and decomposition:
An equation with inexact numeric coefficients:
Multiple roots are repeated the corresponding number of times:
Find roots over the integers modulo 7:
 Options   (10)
By default Roots uses the general formulas for solving cubic equations in radicals:
With Cubics->False, Roots does not use the general formulas for solving cubics in radicals:
Solving this cubic equation in radicals does not require the general formulas:
Use to specify the left-hand side of the returned equations:
Find roots over the integers modulo 12:
With Multiplicity->n, the multiplicity of each root is multiplied by n:
By default Roots uses the general formulas for solving quartic equations in radicals:
With Quartics->False, Roots does not use the general formulas for solving quartics:
Solving this quartic equation in radicals does not require the general formulas:
Specify equations satisfied by symbolic parameters:
Solutions returned by Roots satisfy the equation:
Use ToRules to convert equations returned by Roots to replacement rules:
Solve uses Roots to find solutions of univariate equations and returns replacement rules:
Roots finds all complex solutions:
Use Reduce to find solutions over specified domains:
Use FindInstance to find one solution:
Use Solve or Reduce to find solutions of systems of multivariate equations:
Use Reduce to find solutions of systems of equations and inequalities:
Use NRoots to find numeric approximations of roots of a univariate equation:
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