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Quadratic Solver
Solve ax² + bx + c = 0 and see the discriminant, the roots and the vertex of the parabola.
Solve a quadratic equation
Equation: —
Discriminant: —
Nature of the roots: —
Roots: —
Vertex: —
Axis of symmetry: —
Sum and product of the roots: —
How to use the Quadratic Solver
- Type the coefficients a, b and c of your equation.
- The discriminant and the roots are worked out as you type.
- Read the vertex and axis of symmetry to see where the parabola turns.
Features
- Real roots, a double root or complex roots
- Discriminant and the nature of the roots
- Vertex and axis of symmetry of the parabola
- Handles a = 0 by solving the linear case
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Frequently Asked Questions
Common questions about the free online quadratic solver.
It evaluates the discriminant b squared minus 4ac. When it is positive there are two real
roots, when it is zero there is one repeated root and when.
x equals minus b plus or minus the square root of b squared minus 4ac, all divided by 2a.
It tells you how many real solutions exist. A positive value means two, zero means one and a
negative value means the roots are a complex conjugate.
They are written in the form a plus bi, where i is the imaginary unit and i squared equals
minus one.
The vertex x coordinate is minus b divided by 2a. Substituting it back into the equation
gives the y coordinate, and the tool shows both.
The equation is no longer quadratic, so the tool solves the remaining linear equation bx + c
= 0 instead and tells you.
Yes. Every coefficient accepts decimals and negative values, and results are rounded to six
decimal places.
Substitute each root back into the original equation. The sum and product of the roots shown
by the tool also let you verify them quickly.
No, the calculation happens entirely in your browser.
Last updated: October 10, 2026