Quadratic Equation Solver interactive tool
Equation form:
ax² + bx + c = 0
Δ = b² − 4ac determines whether the roots are real and distinct, real and repeated, or complex.
Discriminant \(b^2 - 4ac\) is positive, so the equation has two distinct real roots.
What Is Quadratic Equation Solver?
A quadratic equation solver is a focused algebra tool that finds the roots (solutions) of equations in the form ax² + bx + c = 0. These equations appear everywhere in school math, physics word problems, and optimization tasks.
How the Quadratic Formula Works
The standard way to solve any quadratic is to apply the quadratic formula:
x = (−b ± √(b² − 4ac)) / (2a)
The expression under the square root, b² − 4ac, is called the discriminant. It tells you how many real roots your quadratic has and whether you will see complex numbers.
- Δ > 0 → two distinct real roots.
- Δ = 0 → one repeated real root.
- Δ < 0 → two complex conjugate roots.
Why Use an Online Quadratic Equation Solver?
This quadratic equation calculator is perfect for checking algebra homework, exploring how changing coefficients affects the roots, or quickly solving word problems that reduce to ax² + bx + c = 0. Because it runs entirely in your browser, you can safely experiment with negative, fractional, or large coefficients without worrying about your data being stored anywhere.
How To Use the Quadratic Equation Solver
- Enter the coefficients a, b, and c for your quadratic equation in the form ax² + bx + c = 0.
- Check that the value of a is non-zero so the equation is truly quadratic.
- Review the discriminant value to see whether the equation has two real roots, one repeated real root, or two complex roots.
- Read the calculated roots in the results card, including complex values when the discriminant is negative.
- Use the Example button to load a sample quadratic, or Reset to clear all three coefficient fields.