Quadratic Equation Solver
Enter finite coefficients a, b, and c locally in your browser to see roots and the discriminant.
For a ≠ 0: ax² + bx + c = a(x + b/(2a))² + c − b²/(4a). Setting this expression to zero gives an equivalent equation. Displayed coefficients are rounded.
A QUICK WALKTHROUGH
How to use this tool
- Enter a, b, and c.
- Choose the displayed decimal places.
- Review real roots, complex roots, or the degenerate result.
Completing the square
For a ≠ 0: ax² + bx + c = a(x + b/(2a))² + c − b²/(4a). Setting this expression to zero gives an equivalent equation. Displayed coefficients are rounded. OpenStax: https://openstax.org/books/algebra-and-trigonometry-2e/pages/2-5-quadratic-equations
Degenerate cases
When a=0, the tool solves the resulting linear equation. When b is also zero, it reports no solution or that every real number is a solution.
Rounding and precision
Calculations use JavaScript number arithmetic, and displayed values are rounded to the selected decimal places. Floating-point precision limits significant digits for extreme values.
GOOD TO KNOW
Common questions
Can I enter decimal coefficients?
Yes, as long as all three coefficients are finite numbers.