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Solve ax² + bx + c = 0.
A quadratic equation solver finds the roots (solutions) of ax² + bx + c = 0 using the quadratic formula, and reports the discriminant that tells you how many real roots exist.
Quadratics model projectile paths, areas, optimisation and many physics and engineering relationships, so solving them quickly is a common need.
The discriminant D = b² − 4ac: if D > 0 there are two real roots, if D = 0 one repeated root, and if D < 0 no real roots (the roots are complex).
It is b² − 4ac, the expression under the square root. Its sign reveals whether there are two real roots, one repeated real root, or no real roots.
There are no real solutions; the parabola does not cross the x-axis. The roots are a pair of complex conjugates.
Yes, for any quadratic with a ≠ 0. Factoring or completing the square can be faster in simple cases, but the formula always works.