Roots
Roots[lhs==rhs,var]
yields a disjunction of equations which represent the roots of a polynomial equation.
Details and Options
- Roots uses Factor and Decompose in trying to find roots.
- 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.
Examples
open allclose allScope (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:
Options (10)
Cubics (3)
Quartics (3)
Properties & Relations (5)
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:
Text
Wolfram Research (1988), Roots, Wolfram Language function, https://reference.wolfram.com/language/ref/Roots.html.
CMS
Wolfram Language. 1988. "Roots." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Roots.html.
APA
Wolfram Language. (1988). Roots. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Roots.html