Quadratic Equation Solver

The roots of a quadratic equation, real or complex, with the discriminant and the vertex of the parabola.

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How to do it

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About this tool

Enter the coefficients a, b and c of ax² + bx + c = 0. The solver finds both roots using the quadratic formula, tells you the discriminant and shows the vertex and axis of symmetry. If the discriminant is negative, the roots are shown as complex numbers.

Frequently asked questions

What is the discriminant?

b² − 4ac. If it is positive there are two real roots, if zero one repeated root, if negative two complex roots.

What if a is 0?

Then it is not a quadratic equation. It becomes a straight line, so a must not be zero.

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