Quadratic Solver
Roots of ax² + bx + c = 0, real or complex.
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The formula
x = (−b ± √(b² − 4ac)) / 2a
The quadratic formula solves any equation of the form ax² + bx + c = 0. The discriminant b² − 4ac decides the shape of the answer before you finish: positive gives two real roots where the parabola crosses the x-axis, zero gives one touching point, and negative means it never crosses, so the roots are complex.
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Frequently asked questions
What does the discriminant tell me?+
If b²−4ac is positive there are two real roots, zero gives one repeated root, and negative gives a complex-conjugate pair.
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