Enter the coefficients a, b and c for ax squared plus bx plus c equals 0. The calculator returns the discriminant and both roots, real or complex, with the steps.
Equation solved: a x squared + b x + c = 0.
Any quadratic equation can be written as a x squared plus b x plus c equals 0, with a not equal to zero. The quadratic formula gives both solutions directly.
The piece under the radical, b squared minus 4ac, is the discriminant. Its sign decides whether the roots are two real numbers, one repeated number, or a conjugate pair of complex numbers.
For a fuller derivation by completing the square, see Wolfram MathWorld on the quadratic formula.
x = (-b plus or minus sqrt(b^2 - 4ac)) / 2a. It solves any equation in the form ax^2 + bx + c = 0 once you know a, b and c.
The discriminant is b^2 - 4ac. Positive gives two real roots, zero gives one repeated root, and negative gives a pair of complex roots.
When b^2 - 4ac is negative, the square root is imaginary. The roots take the form p plus or minus qi, which this tool reports automatically.
Then the equation is not quadratic but linear: bx + c = 0, which solves to x = -c / b. The tool handles this case too.
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