[di-skrim-uh-nuh
nt] 
| a relatively simple expression that determines some of the properties, as the nature of the roots, of a given equation or function. |
[dis-krim-uh-nan-tl] , adjective | dis·crim·i·nant (dĭ-skrĭm'ə-nənt) n. An expression used to distinguish or separate other expressions in a quantity or equation. |
discriminant
in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation ax2+bx+c=0, the discriminant is b24ac; for a cubic equation x3+ax2+bx+c=0, the discriminant is a2b2+18abc4b34a3c27c2. The roots of a quadratic or cubic equation with real coefficients are real and distinct if the discriminant is positive, are real with at least two equal if the discriminant is zero, and include a conjugate pair of complex roots if the discriminant is negative. A discriminant can be found for the general quadratic, or conic, equation ax2+bxy+cy2+dx+ey+f=0; it indicates whether the conic represented is an ellipse, a hyperbola, or a parabola.
Learn more about discriminant with a free trial on Britannica.com.