Sum and Product of Roots Calculator

About this calculator

For any quadratic ax² + bx + c = 0, Vieta’s formulas give the sum and product of the two roots without ever solving for them individually: the sum of roots equals −b/a, and the product equals c/a. The discriminant, b² − 4ac, meanwhile reveals what kind of roots exist — positive means two distinct real roots, zero means one repeated real root, and negative means a complex-conjugate pair.

This calculator plugs your coefficients into all three relationships at once. It’s a quick shortcut in algebra coursework for checking a factored quadratic or building one from known roots, and it’s the underlying logic behind problems that ask you to construct an equation given only the sum and product of its solutions.