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
Doubling the cube at solving what they saw as an obstinate but soluble problem. However, the nonexistence of a solution was finally proven by Pierre Wantzel in 1837. In algebraic terms, doubling a unit cube requires the construction of a line segment of length , where ; in other words, . This is because a cube of side length 1 has a volume of , and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2. The impossibility of doubling the cube is therefore equivalent to the statement that is not a constructible