Root-finding algorithm cubic polynomial may involve non-real cube roots). For polynomials of degree five or higher Abel–Ruffini theorem asserts that there is, in general, no radical expression of the roots. So, except for very low degrees, root finding of polynomials consists of finding approximations of the roots. By the fundamental theorem of algebra, one knows that a polynomial of degree has at most real or complex roots, and the this number is reached for almost all polynomials. It follows that the problem of root finding for polynomials may be split in three different subproblems; For finding one root, Newton's method and other
Nth root real number is a positive real number, negative numbers do not have real square roots. However, for every negative real number there are two imaginary square roots. For example, the square roots of −25 are 5"i" and −5"i", where "i" represents a number whose square is . A cube root of a number "x" is a number "r" whose cube is "x": Every real number "x" has exactly one real cube root, written formula_4. For example, Every real number has two additional complex cube roots. Expressing the degree of an "n"th root in its exponent form, as in formula_37, makes