What is Quadratic Equation Solver?
The Quadratic Equation Solver finds the roots (solutions) of equations in the form ax² + bx + c = 0 using the quadratic formula. This is one of the most fundamental algebraic operations taught in high school and used extensively in physics, engineering, and economics.
The discriminant (b²−4ac) determines the nature of roots: positive = 2 real roots, zero = 1 repeated root, negative = 2 complex roots.
Formula
x = (−b ± √(b²−4ac)) / 2a Discriminant = b² − 4ac D > 0: Two distinct real roots D = 0: One repeated root (x = −b/2a) D < 0: Two complex conjugate roots Vertex: x = −b/2a, y = f(−b/2a) Example: x² − 5x + 6 = 0 D = 25 − 24 = 1 x = (5 ± 1)/2 → x = 3 or x = 2
How to use this Quadratic Equation Solver?
1. Enter coefficients a, b, and c. 2. See both roots, discriminant, and vertex. 3. Default example: x²−5x+6=0 gives roots x=2 and x=3.