Quadratic Formula Calculator
Enter the coefficients a, b and c of a quadratic equation to find its roots using the quadratic formula.
Quadratic Formula Calculator
Solves ax² + bx + c = 0 for its real roots, discriminant and root type.
This calculator applies the quadratic formula x = (-b ± √(b²-4ac)) / 2a directly to whatever coefficients you enter, computing the discriminant first to decide how many real solutions exist. It's useful for checking algebra homework, factoring problems, or any situation — physics, engineering, finance — where you land on a quadratic equation and need its roots quickly. When the discriminant is negative the calculator reports zero for both roots since real-valued roots don't exist in that case.
Example
- With the default values shown above, this calculator returns: Discriminant (b² - 4ac) ≈ 1; Root 1 (x₁) ≈ 2; Root 2 (x₂) ≈ 1; Nature of Roots = 1.0.
Frequently Asked Questions
What does the discriminant tell me?
The discriminant b²-4ac tells you how many real roots the equation has: positive means two distinct real roots, zero means one repeated root, and negative means no real roots (the roots are complex).
What happens if a is 0?
If a is 0 the equation is no longer quadratic (it becomes linear), so this calculator assumes a is non-zero; enter a small non-zero value if you need a near-linear case.
Can the roots be negative?
Yes, roots can be negative, positive, zero, or (when the discriminant is negative) not real at all — the calculator reports 0 for both roots in that case since they only exist in the complex plane.
Sources
- Standard formula, publicly documented method