discriminant
UK: dɪˈskrɪmɪnənt | US: dɪˈskrɪmɪnənt
n. (Mathematics) A function of the coefficients of a polynomial equation whose value gives information about the roots of the polynomial (e.g., real, distinct, or complex).
The word "discriminant" originates from the Latin verb discriminare (to divide or distinguish), derived from discrimen (separation). The prefix dis- (apart) combines with crimin- (from cernere, to sift or decide), reflecting the mathematical function's role in "separating" or distinguishing between types of polynomial roots. The suffix -ant nominalizes the term, indicating an agent or tool of discrimination.
The discriminant of a quadratic equation determines whether its roots are real or complex.
A positive discriminant indicates two distinct real solutions.
In algebra, calculating the discriminant helps classify the nature of solutions.
If the discriminant is zero, the equation has a repeated root.
The discriminant provides critical insight into the behavior of polynomial functions.