How to Use the Quadratic Equation Solver
The Quadratic Equation Solver finds the roots of ax²+bx+c=0 given the three coefficients a, b, and c. It calculates the discriminant, identifies the root type, and shows both roots — real or complex. Use it for math exams, physics, engineering, and financial modeling.
The discriminant D = b²−4ac determines the nature of the roots. D > 0 gives two distinct real roots, D = 0 gives a repeated root, and D < 0 gives two complex conjugate roots.
The Quadratic Formula
x = (−b ± √D) / 2a, where D = b²−4ac. Example: x²−5x+6=0 → D = 25−24 = 1 → roots x = 3 and x = 2. Complex example: x²+x+1=0 → D = 1−4 = −3 → roots −0.5 ± (√3/2)i.
Frequently Asked Questions
Complex roots are solutions in the complex number system. In real-number contexts (e.g., physical measurements), D < 0 means no real solution exists.
When D = 0, both roots are equal: x = −b/2a. The parabola just touches the x-axis at one point.
Yes. For example, a=1.5, b=−2.7, c=0.5 are calculated correctly.