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.
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