x² Quadratic Equation Solver

ax² + bx + c = 0

Roots (Solutions)

The Quadratic Formula

A quadratic equation has the form ax² + bx + c = 0, where a ≠ 0. The solutions (roots) are found using the quadratic formula.

x = (−b ± √(b² − 4ac)) / 2a
Discriminant D = b² − 4ac

Types of Roots (based on Discriminant)

D > 0
Two distinct real roots
D = 0
One repeated real root
D < 0
Two complex roots

Frequently Asked Questions

How do you solve x² - 5x + 6 = 0? ▼
For a=1, b=−5, c=6: D = 25−24 = 1. x = (5±1)/2. So x₁ = 3, x₂ = 2. Check: (x−2)(x−3) = 0.
What is the discriminant? ▼
The discriminant is D = b² − 4ac. It tells you the nature of the roots: D>0 gives two real roots, D=0 gives one repeated root, D<0 gives complex roots.
What if a=0 in a quadratic? ▼
If a=0, the equation becomes linear (bx + c = 0), not quadratic. The quadratic formula requires a ≠ 0.