Quadratic Equation Solver
Quadratic Equation Solver
The quadratic equation solver finds the roots (x-intercepts) of any second-degree polynomial equation using the quadratic formula.
Conversion Formula
x = (-b ± √(b² - 4ac)) / 2a. The ± means there are potentially two solutions. The discriminant (b² - 4ac) determines if roots are real, repeated, or complex.
Step-by-Step Examples
a=1, b=-5, c=6 = x₁=3, x₂=2
Discriminant = 25-24 = 1. Roots: (5±1)/2 → x₁=3, x₂=2.
a=1, b=-4, c=4 = x₁=2, x₂=2
Discriminant = 16-16 = 0. One repeated root: x = 4/2 = 2.
Frequently Asked Questions
What is the quadratic formula?
x = (-b ± √(b² - 4ac)) / 2a. It gives the solutions for any equation of the form ax² + bx + c = 0.
What is the discriminant?
The discriminant is b² - 4ac. It determines the nature of the roots: positive means two real roots, zero means one repeated root, negative means no real roots.
What if the discriminant is negative?
The equation has no real solutions. The roots are complex (imaginary) numbers.
Can a be zero?
No. If a = 0, the equation is linear (bx + c = 0), not quadratic.
What does it mean to have a repeated root?
When the discriminant is zero, both roots are the same value. The parabola touches the x-axis at exactly one point.