quadratic, mathematical expression of the second degree in one or more unknowns (see polynomial). The general quadratic in one unknown has the form ax²+bx+c, where a, b, and c are constants and x is the variable. A quadratic equation ax²+bx+c=0 always has two roots, not necessarily distinct; these may be real or complex (see number). The quadratic formulagives the roots of any quadratic equation in terms of its coefficients a, b, and c. The expression b²-4ac is called the discriminant and vanishes when the two roots coincide. If a, b, and c are real and the discriminant is not less than zero, the roots are real.