Quadratic Equation Solver

How this quadratic equation solver works

Enter the coefficients a, b, and c for the equation ax² + bx + c = 0. The solver uses the quadratic formula and shows the discriminant, root type, and both roots (real or complex).

The quadratic formula

x = (−b ± √(b² − 4ac)) / (2a)

The discriminant

The value D = b² − 4ac determines the nature of the roots:

• D > 0: Two distinct real roots
• D = 0: One repeated real root (the parabola touches the x-axis at its vertex)
• D < 0: Two complex conjugate roots (no real x-intercepts)