How to Use
Type the values of a, b, and c for your equation ax² + bx + c = 0. 'a' must not be zero.
Use "Solve Equation" for roots, "Form from Roots" to build an equation, or "Nature of Roots" to check the discriminant.
Click Calculate to see the roots, discriminant, Vieta's formulas, and complete step-by-step working.
Frequently Asked Questions
The quadratic formula is x = (−b ± √(b² − 4ac)) / 2a. It solves any quadratic equation ax² + bx + c = 0 where a ≠ 0. The ± sign gives two roots.
The discriminant is D = b² − 4ac. If D > 0: two distinct real roots. If D = 0: one repeated real root. If D < 0: two complex conjugate roots (no real solution). D is the key to predicting root type without solving.
For ax² + bx + c = 0 with roots α and β: Sum α + β = −b/a and Product αβ = c/a. These are Vieta's formulas. In SSC and bank exams, questions often ask you to find these without computing individual roots.
If α and β are the roots, the equation is x² − (α + β)x + αβ = 0. Simply compute the sum and product of the given roots and substitute. Use the "Form from Roots" tab above.
When D = b² − 4ac < 0, the equation has no real roots. The roots become complex conjugates: x = −b/2a ± i√|D|/2a. Complex roots always occur in pairs and are equal in magnitude.
Yes. A quadratic equation must have x² as its highest power and the coefficient 'a' must be non-zero. If a = 0, it becomes a linear equation (bx + c = 0), not quadratic.