This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 Roots Roots[ lhs == rhs , var ] yields a disjunction of equations which represent the roots of a polynomial equation. 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: 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. See the Mathematica book: Section 1.5.7, Section 3.4.1. See also: Solve, NSolve, FindRoot, ToRules, Root, Factor, Decompose, InterpolatingPolynomial. Related package: Algebra`RootIsolation`. Further Examples The roots of some cubic and quartic polynomials can be expressed in terms of radicals using Cardano's formulas. The results, while explicit, are often very complicated. In[1]:= Out[1]= You can use algebraic numbers instead. In[2]:= Out[2]= If any one of the coefficients of the polynomial is inexact, Roots finds approximate roots. In[3]:= Out[3]= In[4]:= Out[4]= In[5]:= You can find the roots of univariate polynomials for any finite modulus. When the modulus is not prime there may be more roots than the degree of the polynomial. This is in contrast to the fundamental theorem of algebra. It states that over the complexes there are as many roots (counting multiplicity) as the degree. In[6]:= Out[6]= In[7]:= Out[7]= In[8]:= Out[8]=