Free online quadratic equation solver. Solve ax²+bx+c=0 with step-by-step solutions. Shows real and complex roots, discriminant, vertex, and factorization. Pure frontend.
Solve ax² + bx + c = 0
The quadratic formula x = [-b ± √(b² - 4ac)] / (2a) solves any quadratic equation ax² + bx + c = 0. The discriminant Δ = b² - 4ac determines the type of roots.
If Δ > 0: two distinct real roots. If Δ = 0: one double real root. If Δ < 0: two complex conjugate roots.
The vertex is the turning point of the parabola at x = -b/(2a). It represents the minimum (a>0) or maximum (a<0) point of the quadratic function.
Yes! When the quadratic has integer roots and whole coefficients, the solver displays the factored form automatically.
When the discriminant is negative, the roots involve the imaginary unit i (√-1). They come as conjugate pairs: p + qi and p - qi.