discriminants

noun

1. 1.An expression that gives information about the roots of a polynomial; for example, the expression D = b2 - 4ac determines whether the roots of the quadratic equation ax2 + bx + c = 0 are real and distinct (D > 0), real and equal (D = 0) or complex (D < 0).
2. 2.The invariant (on the vector space of forms of degree d in n variables) that vanishes exactly when the corresponding hypersurface in Pn-1 is singular.