Toolstia / Quadratic equation solver
Quadratic equation solver
Enter the three coefficients of a quadratic equation and get both solutions at once, including complex solutions when the parabola does not cross the x-axis. The discriminant, the vertex and the y-intercept are shown too.
Solve ax² + bx + c = 0
How it works
- Enter a, b and c from ax² + bx + c = 0.
- Read the two roots.
- Check the discriminant and vertex for the shape of the parabola.
The quadratic formula
x = (−b ± √(b² − 4ac)) ÷ 2a. The part under the square root, b² − 4ac, is called the discriminant.
What the discriminant tells you
A positive discriminant gives two different real roots, zero gives one repeated root, and a negative discriminant gives two complex roots that are conjugates of each other.
Accurate for extreme values
The tool avoids the subtraction of nearly equal numbers that makes the textbook formula lose accuracy, so small roots stay precise even when b is very large.
The vertex
The turning point of the parabola is at x = −b ÷ 2a. It is the minimum when a is positive and the maximum when a is negative.
Questions
What if a is zero?
Then the equation is not quadratic. The tool solves the straight line bx + c = 0 instead.
Can the roots be complex?
Yes. When the discriminant is negative the roots are shown in the form p + qi.
Is anything uploaded?
No. Your input stays in your browser and is never sent anywhere.