Quadratic Formula Calculator
Solve any quadratic equation ax² + bx + c = 0, including complex roots.
First root (x₁)
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Second root (x₂)
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Discriminant (b² − 4ac)
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Nature of roots
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Vertex
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Axis of symmetry
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Factored form
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Results update as you type.
About this calculator
This calculator solves a quadratic equation ax² + bx + c = 0 using the quadratic formula x = (−b ± √(b² − 4ac)) / 2a. The discriminant b² − 4ac tells you the nature of the roots: positive gives two real roots, zero gives one repeated root, and negative gives a pair of complex conjugate roots.
Frequently asked questions
What does the discriminant tell me?
The discriminant b² − 4ac decides the roots: positive means two real solutions, zero means one repeated solution, and negative means two complex solutions.
What if a is zero?
Then the equation is linear, not quadratic, and the quadratic formula does not apply. Enter a non-zero value for a.
Results are estimates for general guidance only, not financial, medical or tax advice.