The roots (sometimes also called "zeros") of an equation
are the values of for which the equation is satisfied.
Roots which belong to certain sets are usually preceded by a modifier to indicate such, e.g., is called a rational root, is called a real root, and is called a complex root.
The fundamental theorem of algebra states that every polynomial equation of degree has exactly complex roots, where some roots may have a multiplicity greater than 1 (in which case they are said to be degenerate). In the Wolfram Language, the expression Root[p(x), k] represents the th root of the polynomial, where , ..., is an index indicating the root number in the Wolfram Language's ordering.
The roots of a complex function can be obtained by separating it into its real and imaginary plots and plotting these curves (which are related by the Cauchy-Riemann equations) separately. Their intersections give the complex roots of the original function. For example, the plot above shows the curves representing the real and imaginary parts of , with the three roots indicated as black points.
Householder (1970) gives an algorithm for constructing root-finding algorithms with an arbitrary order of convergence. Special root-finding techniques can often be applied when the function in question is a polynomial.
for which the equation is satisfied. 
which belong to certain sets are usually preceded by a modifier to indicate such, e.g., 
is called a rational root, 
is called a real root, and 
is called a complex root. 
has exactly 
complex roots, where some roots may have a multiplicity greater than 1 (in which case they are said to be degenerate). In the Wolfram Language, the expression Root[p(x), k] represents the 
th root of the polynomial 
, where 
, ..., 
is an index indicating the root number in the Wolfram Language's ordering. 
th root" 
of a complex number 
is known as an nth root. 
, with the three roots indicated as black points. 