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:
“More than a decade after our fellow citizens began bedding down on the sidewalks, their problems continue to seem so intractable that we have begun to do psychologically what government has been incapable of doing programmatically. We bring the numbers down—not by solving the problem, but by deciding it’s their own damn fault.”
—Anna Quindlen (b. 1952)