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.
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.