Quadratic Equation Solver
Use this quadratic equation calculator to solve ax² + bx + c = 0 and review the roots, discriminant and vertex from the coefficients you enter.
Roots
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Discriminant—
Vertex—
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How it works
x = (−b ± √(b² − 4ac)) / 2aHow to use the Quadratic Equation Calculator
Enter the values of a, b and c, then check the roots and discriminant shown by the tool. The discriminant indicates whether the equation has two real roots, one repeated root or complex roots.
Use the working below the result to check each step. If a is zero, the equation is linear rather than quadratic.
Frequently Asked Questions
What if the discriminant is negative?
The equation has two complex roots, shown in the form p ± qi.
What if a is 0?
It is no longer quadratic. The solver treats it as the linear equation bx + c = 0.
Can I use the result as an exact answer?
Treat it as an estimate or check unless the page and the rules that apply to you confirm otherwise. Rounding, fees and personal details can change the final result.