Discriminant
SAT glossary · Course Foundations
Definition
The quantity b2 -4ac under the radical in the quadratic formula. It counts real solutions: positive gives two, zero gives one, negative gives none. The tool for every "how many solutions" and tangency item with an unknown constant.
Discriminant in plain English
The discriminant is the expression b^2-4ac that lives under the square root sign in the quadratic formula, and it acts like a quick messenger that tells you how many real solutions a quadratic equation has — without you having to actually solve the whole thing. If it comes out positive, there are two real solutions; if it's exactly zero, there's just one (a repeated one); and if it's negative, there are no real solutions at all (the square root of a negative number isn't a real number). This makes the discriminant your go-to tool anytime a question asks 'how many solutions does this have' or involves a mystery constant and the idea of a line just barely touching a curve (tangency).
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