Solve a quadratic equation ax² + bx + c = 0 for its roots. Enter the three coefficients.
Roots
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Solutions for x.Usage Tip
If the discriminant is a perfect square, the roots are rational and the quadratic factors neatly.
THE MATH
x = (−b ± √(b² − 4ac)) ÷ 2a
The discriminant b² − 4ac sets the number of real roots
The discriminant b² − 4ac sets the number of real roots
The quadratic formula solves any quadratic equation.
The discriminant tells the story: positive gives two real roots, zero gives one, negative gives a complex pair.
The discriminant tells the story: positive gives two real roots, zero gives one, negative gives a complex pair.
Coefficient a cannot be zero (that would be a linear equation).
Complex roots are shown in a ± bi form.
The vertex x-coordinate is −b ÷ 2a.
Complex roots are shown in a ± bi form.
The vertex x-coordinate is −b ÷ 2a.