Solve ax² + bx + c = 0 — real and complex roots with step-by-step work
This calculator solves quadratic equations of the form ax² + bx + c = 0 using the quadratic formula. It computes the discriminant to determine the nature of the roots — two real roots when D > 0, one real root when D = 0, and complex conjugate roots when D < 0 — with a full step-by-step breakdown.
The discriminant (D = b² − 4ac) determines the nature of roots. If D > 0, there are two distinct real roots. If D = 0, one real root (double root). If D < 0, two complex conjugate roots.
If a = 0, the equation is no longer quadratic — it becomes linear (bx + c = 0). The calculator requires a non-zero value for a.