discriminant

1. (algebra) 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. (geometry) 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.