About Quadratic Formula Calculator
The quadratic formula is used to solve quadratic equations of the form ax² + bx + c = 0. This calculator finds the roots (solutions) of the equation and provides step-by-step explanations.
The Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
Where:
- a is the coefficient of x² (must not be zero)
- b is the coefficient of x
- c is the constant term
- Δ = b² - 4ac is the discriminant
Understanding the Discriminant
- Δ > 0: Two distinct real rootsThe parabola crosses the x-axis at two points
- Δ = 0: One real root (repeated root)The parabola touches the x-axis at exactly one point
- Δ < 0: Two complex conjugate rootsThe parabola does not intersect the x-axis
How to Use
- Enter the coefficient a (for x² term) - must be non-zero
- Enter the coefficient b (for x term)
- Enter the coefficient c (constant term)
- Click "Solve Equation" to see the results
- Review the discriminant, root types, and complete solution steps
Example
Solve: x² - 3x + 2 = 0 (where a=1, b=-3, c=2)
- Discriminant: Δ = (-3)² - 4(1)(2) = 9 - 8 = 1
- Since Δ > 0, there are two real roots
- x₁ = (3 + √1) / 2 = (3 + 1) / 2 = 2
- x₂ = (3 - √1) / 2 = (3 - 1) / 2 = 1
- Solutions: x = 1 or x = 2