The quartic formula is a name sometimes given to one of the related explicit formulas for the four roots z_1, ..., z_4 of an arbitrary quartic equation with real coefficients z^4 + a_3 z^3 + a_2 z^2 + a_1 z + a_0 = 0. Let y_1 be a real root of the resolvent cubic equation y^3 - a_2 y^2 + (a_1 a_3 - 4a_0) y + (4a_2 a_0 - a_1^2 - a_3^2 a_0) = 0.

quadratic equation | quadratic formula | quartic equation