Quadratic Formula Calculator
ax² + bx + c = 0
How to Use the Quadratic Formula Calculator
This calculator solves for the roots of a quadratic equation in the standard form ax² + bx + c = 0. To find the solutions (x-intercepts), follow these steps:
- Enter the value for a (the coefficient of the x² term). Note: 'a' cannot be zero.
- Enter the value for b (the coefficient of the x term).
- Enter the value for c (the constant or numerical term).
- Click "Solve Equation" to find the real or complex roots.
Understanding the Formula
The quadratic formula is a fundamental tool in algebra used to find the solutions to any second-degree polynomial equation. The formula is expressed as:
x = [-b ± √(b² – 4ac)] / 2a
The Role of the Discriminant (D)
The term inside the square root, b² – 4ac, is known as the discriminant. It determines the nature of the roots:
- D > 0: There are two distinct real roots.
- D = 0: There is exactly one real root (a repeated root).
- D < 0: There are no real roots, only two complex (imaginary) roots.
Step-by-Step Example
Let's solve the equation x² + 5x + 6 = 0:
- Identify: a = 1, b = 5, c = 6
- Calculate Discriminant: 5² – 4(1)(6) = 25 – 24 = 1
- Apply Formula: x = [-5 ± √1] / 2(1)
- Root 1: (-5 + 1) / 2 = -2
- Root 2: (-5 – 1) / 2 = -3
The solutions for this equation are x = -2 and x = -3.