Cubic Equation

A cubic equation has the form a x cubed plus b x squared plus c x plus d equals zero, where a is not zero, and every cubic equation has exactly three roots when multiplicity is counted, though not all of them need be real; if the coefficients are real, at least one root is guaranteed to be real. Its solutions can be found algebraically with Cardano's formula, which uses arithmetic together with square and cube roots, geometrically by a method going back to Omar Khayyam's work, trigonometrically, or by numerical approximation. Cubic equations were already known to the Babylonians, Greeks, Chinese, Indians and Egyptians, but a complete algebraic solution was not published until the Renaissance, when Gerolamo Cardano set out del Ferro's and Tartaglia's methods in 1545.