Discriminant Calculator

How This Is Calculated

For a quadratic ax² + bx + c = 0, the discriminant D = b² − 4ac decides everything about the roots without solving for them: positive means two distinct real roots, zero means one repeated root, negative means no real roots. See the full reasoning in the Complex Numbers & Quadratic Equations chapter guide, or use the Quadratic Equation Solver to find the actual roots.