Solve ax² + bx + c = 0 — find roots, discriminant, vertex, and more
Solves quadratic equations of the form ax² + bx + c = 0 using the quadratic formula. Returns both real roots when the discriminant is non-negative, or complex roots when it is negative.
x = (−b ± √(b² − 4ac)) / 2a
a, b, ccoefficients in ax² + bx + c = 0Δ (discriminant)b² − 4ac; positive → two real roots, zero → one repeated root, negative → complex rootsFor ax² + bx + c = 0: x = (-b ± √(b² - 4ac)) / 2a. The ± gives two solutions. The expression b² - 4ac is called the discriminant.
If b² - 4ac > 0: two real, distinct solutions. If b² - 4ac = 0: one real repeated solution. If b² - 4ac < 0: two complex conjugate solutions with no real roots.
Factor when the equation has small integer coefficients and rational roots. Use the quadratic formula when factoring is hard, coefficients are decimals, or solutions are irrational or complex.