Enter a, b and c from your equation (ax² + bx + c = 0) and get the roots instantly — with the discriminant and the type of roots shown, not just a number.
Quadratic Equation Solver
How It’s Calculated
Every quadratic equation ax² + bx + c = 0 is solved using the quadratic formula: x = (−b ± √(b² − 4ac)) / 2a. The expression under the square root — b² − 4ac — is the discriminant, and its sign tells you what kind of roots to expect before you even finish the calculation: positive means two real, distinct roots; zero means one repeated real root; negative means two complex conjugate roots.
Worked Example
For x² − 5x + 6 = 0: a = 1, b = −5, c = 6. Discriminant = (−5)² − 4(1)(6) = 25 − 24 = 1. Since 1 > 0, there are two real roots: x = (5 ± 1) / 2, giving x₁ = 3 and x₂ = 2.
Frequently Asked Questions
Q: What if a is 0?
Then the equation isn’t quadratic — it’s linear (bx + c = 0), and this tool won’t solve it.
Q: What does a negative discriminant mean?
The equation has no real roots — the parabola never crosses the x-axis. The two roots are complex conjugates.
This is exactly the chapter Daniel Sir covers in 1st PUC Complex Numbers & Quadratic Equations — including the exam-specific mistakes students make with the discriminant. See how Daniel Classes teaches 1st and 2nd PUC Mathematics →