Quadratic Formula Calculator

Find the roots of any quadratic equation. This tool handles real and imaginary solutions and shows you the discriminant value used in the calculation.

Formula: x = [-b ± √(b² - 4ac)] / 2a
For x² - 5x + 6 = 0: a=1, b=-5, c=6 x = [5 ± √(25 - 24)] / 2 = [5 ± 1] / 2 Roots: x₁=3, x₂=2.

What is the quadratic formula?

The quadratic formula is x = [-b ± √(b² - 4ac)] / (2a). It is used to find the solutions (roots) of any quadratic equation in the form ax² + bx + c = 0.

What is the discriminant?

The discriminant is the part of the formula under the square root: b² - 4ac. It determines the nature of the roots: if it is positive, there are two real roots; if zero, one real root; if negative, two complex roots.

Can this formula solve any quadratic equation?

Yes! The quadratic formula is a universal method that works for any quadratic equation, even if it cannot be factored easily by hand.

What happens if "a" is zero?

If a = 0, the equation is no longer quadratic; it becomes a linear equation (bx + c = 0). The quadratic formula only applies when a ≠ 0.