Solving Polynomials
It was once believed that all roots of polynomials could be expressed in terms of radicals and elementary operations; however, while this is true for third degree polynomials (cubics) and fourth degree polynomials (quartics), the Abel-Ruffini theorem (1824) shows that this is not true in general when the degree is 5 or greater. For example, the solutions of the equation
cannot be expressed in terms of radicals. (cf. quintic equation)
For solving any equation of the nth degree numerically, to obtain a result that is arbitrarily close to being exact, see Root-finding algorithm.
Read more about this topic: nth Root
Famous quotes containing the word solving:
“You are right to demand that an artist engage his work consciously, but you confuse two different things: solving the problem and correctly posing the question.”
—Anton Pavlovich Chekhov (1860–1904)