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Solve ax² + bx + c = 0 with the quadratic formula. The discriminant is always shown: positive means two real roots, zero means one repeated root, and negative means a complex conjugate pair (no real solutions).
Real or complex roots of ax² + bx + c = 0 with discriminant.
x = (−b ± √(b² − 4ac)) / 2a
| Symbol | Meaning |
|---|---|
| a | Quadratic coefficient (cannot be zero) |
| b | Linear coefficient |
| c | Constant term |
x² − 5x + 6 = 0 → D = 1, roots x = 3 and x = 2. x² + 1 = 0 → D = −4, roots ±i.
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D > 0: two distinct real roots. D = 0: one repeated root. D < 0: two complex roots, no real solutions.
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Content updated: September 2026