Scrabble?! DISCRIMINANTS

Definitions of DISCRIMINANTS in various dictionaries:

In algebra, the discriminant of a polynomial is a polynomial function of its coefficients, which allows deducing some properties of the roots without computing them. For example, the discriminant of the quadratic polynomial a x 2 + b x + c {\displaystyle ax^{2}+bx+c} is b 2 − 4 a c , {\displaystyle b^{2}-4ac,} which is zero if and only if the polynomial has a double root, and (in the case of real coefficients) is positive if and only if the polynomial has two real roots. More generally, for a polynomial of an arbitrary degree, the discriminant is zero if and only if it has a multiple root, and, in the case of real coefficients, it is positive if and only if the number of non-real roots is a multiple of 4 when the degree is 4 or higher. The discriminant is widely used in number theory, either directly or through its generalization as the discriminant of a number field. For factoring a polynomial with integer coefficients, the standard method consists in first factoring its reduction modulo, a prime number not dividing the discriminant (and not dividing the leading coefficient). In algebraic geometry, the discriminant with respect to one of the variables characterizes the points of a hypersurface where the implicit function theorem does not apply. The term "discriminant" was coined in 1851 by the British mathematician James Joseph Sylvester.