the.com/discriminant

means The expression (commonly b²−4ac for a quadratic) whose sign tells you how many real solutions an equation has — two, one, or none.

from From Latin discriminare, 'to divide, distinguish between,' built from discrimen meaning 'a dividing line' or 'distinction' — itself from the verb discernere, 'to separate' (the same root that gives us 'discern' and 'discriminate'). Mathematicians in the 19th century borrowed the word for exactly this purpose: a single value that separates one kind of outcome from another, deciding — before any solving is done — which 'side' of the quadratic's fate an equation falls on.