What Is Discriminant?
The discriminant is the expression b² − 4ac, found under the square root in the quadratic formula. Its sign tells you what kind of solutions a quadratic equation has before you even solve it: positive means two real solutions, zero means one repeated real solution, and negative means two complex solutions.
Example
For x² − 4x + 4 = 0 (a = 1, b = −4, c = 4), the discriminant is (−4)² − 4(1)(4) = 16 − 16 = 0, so there's exactly one repeated solution.