A quintic equation is a one-variable polynomial equationOver the complex numbers, it has five roots of a polynomial counted with multiplicity of a root, by the fundamental theorem of algebra. Over the real numbers, at least one root is real because the leading odd-degree term makes the polynomial take opposite signs far enough in the two directions.
Some quintics are easy to solve: has roots . The Abel-Ruffini theorem says that a formula by radicals cannot solve the general quintic equation; it does not rule out special factorizations, other special-function descriptions, or numerical root finding. Thus failure of a universal radical formula does not prevent exact or approximate solutions of particular equations.
