Quadratic Formula Calculator
Enter values for a, b, and c in the equation ax² + bx + c = 0.
Equation: 1x² + 0x + 0 = 0
What Is a Quadratic Formula Calculator Online?
A quadratic formula calculator online is a quick tool that solves equations of the form ax² + bx + c = 0. Instead of doing each algebra step manually, you can enter the coefficients and instantly get the roots (solutions), the discriminant, and the type of result.
This is useful for students, teachers, test prep, engineering work, and anyone who needs a fast and accurate way to solve quadratic equations.
Quadratic Formula Used by the Calculator
The expression under the square root, b² - 4ac, is called the discriminant. It tells you how many roots exist and whether they are real or complex.
How to Interpret the Discriminant
- b² - 4ac > 0 → two distinct real roots
- b² - 4ac = 0 → one repeated real root
- b² - 4ac < 0 → two complex conjugate roots
How to Use This Solver
- Type your coefficient values for a, b, and c.
- Click Calculate Roots.
- Read the roots, discriminant, and result classification.
- Use Clear to reset and try another equation.
Example Problems
Example 1: Two Real Roots
For x² - 5x + 6 = 0, we have a=1, b=-5, c=6. The roots are x=2 and x=3.
Example 2: One Repeated Root
For x² - 4x + 4 = 0, the discriminant is zero, so the solution is x=2 (double root).
Example 3: Complex Roots
For x² + 2x + 5 = 0, the discriminant is negative. The roots are complex: x = -1 ± 2i.
Common Mistakes When Solving Quadratics
- Forgetting that a cannot be zero in a true quadratic equation.
- Sign mistakes when substituting negative values for b or c.
- Confusing b² with 2b.
- Not simplifying final roots.
Why Use an Online Quadratic Calculator?
A good online quadratic equation solver saves time and reduces arithmetic errors. It is especially helpful when checking homework, preparing for algebra exams, or validating calculations in science and technical work.
You can still learn the method by hand, but this calculator gives immediate feedback so you can focus on understanding concepts like factoring, discriminant analysis, and graph behavior.