// Number / Math
Quadratic Solver online
Solve ax² + bx + c = 0 - step-by-step with real and complex roots
by
CHUNKY
MUNSTER
MUNSTER
Quadratic Equation Solver: find the roots of any quadratic equation of the form ax² + bx + c = 0. By entering the coefficients, this calculator applies the quadratic formula to determine both real and complex roots while providing a clear breakdown of the discriminant. This is essential for students and professionals working with parabolas and polynomial functions.
The discriminant, calculated as b² − 4ac, determines the nature of the solutions. A positive value indicates two distinct real roots, zero results in one repeated real root, and a negative value reveals a pair of complex-conjugate roots. This math solver handles all these cases automatically using high-precision arithmetic, ensuring accuracy for even complex algebra problems.
The discriminant Δ = b² − 4ac decides the nature of the roots. Δ > 0: two distinct real roots. Δ = 0: one repeated real root. Δ < 0: a pair of complex-conjugate roots. The sign appears in the result panel before the roots themselves.
Yes - when a is zero the equation is linear (bx + c = 0) and the tool returns the single root −c/b. If both a and b are zero it reports that there is no equation to solve.
A negative discriminant gives complex roots. The solver returns them as a real part −b/(2a) and an imaginary part √|Δ|/(2a), as a conjugate pair - the standard output of the quadratic formula over the complex numbers.
It is computed in IEEE-754 double precision, which is accurate to about 15 significant figures. For ill-conditioned equations (a very small relative to b), the formula can lose accuracy on one of the two roots - the citardauq form would do better but is overkill for most inputs.
Whether you are solving for x in a classroom setting or building a simulation, this free online tool provides reliable results. Check out other Number tools at Chunky Munster and bookmark this Quadratic Equation Solver for your next math project.