Quadratic Equation Solver
Solve a quadratic equation for its roots.
Roots of a quadratic
A quadratic equation, where the highest power is a square, can have two, one, or no real solutions. This solves a quadratic for its roots from the coefficients, giving the values that satisfy the equation.
Enter the coefficients to solve the quadratic.
Factoring, the formula, and the graph
There are a few routes to solving a quadratic, and it is useful to know they all give the same answer. Simple quadratics can be factored — spotting two numbers that multiply and add to the right values — which is quick when it works. The quadratic formula always works, whatever the coefficients, which is why it is the reliable fallback. And graphically, the solutions are where the parabola crosses the horizontal axis, which is why a quadratic with no real solutions is one whose curve never touches that axis. The part of the formula under the square root, the discriminant, tells you in advance which case you are in. Seeing that the algebraic solutions and the graph's crossings are the same points ties the symbolic and visual sides of quadratics together.
Quadratic Equation Solver FAQ
How many solutions can a quadratic have?
Two, one, or no real solutions, corresponding to a parabola crossing the horizontal axis twice, touching it once, or missing it entirely.
What are the ways to solve one?
Factoring when it works, the quadratic formula which always works, or graphically as where the parabola crosses the axis — all give the same roots.
Is anything uploaded?
No. The calculation happens in your browser.