Solve ax² + bx + c = 0 with real or complex roots.
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Understanding your result
A positive discriminant gives two real roots, zero gives one repeated root, and a negative value gives a complex conjugate pair.
Formula and method
Roots = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant b² − 4ac determines whether the roots are real and distinct, repeated or complex.
Worked example
x² − 3x + 2 = 0 has roots x = 2 and x = 1.
How to use this tool
- Enter the coefficients a, b and c.
- Press Solve.
Common mistakes to avoid
- Setting a = 0, which makes it a linear, not quadratic, equation.
About the Quadratic Equation Solver
Solve any quadratic equation ax² + bx + c = 0, with real or complex roots, plus the discriminant and vertex.
Frequently asked questions
Does it handle complex roots?
Yes. When the discriminant is negative it reports the complex conjugate roots.