What is the Quadratic Formula?

The quadratic formula provides a universal method for solving any quadratic equation. It gives two solutions (one with +, one with -) and works for all quadratic equations, even those that cannot be factored.

The Formula Explained

a = Coefficient of x²

b = Coefficient of x

c = Constant term

The Discriminant

The expression under the square root, b² - 4ac, is called the discriminant. It tells you about the nature of the solutions:

• Discriminant > 0: Two real solutions
• Discriminant = 0: One real solution (double root)
• Discriminant < 0: Two complex solutions

Step-by-Step Example

Solve: x² - 5x + 6 = 0

Step 1: Identify a=1, b=-5, c=6

Step 2: x = (5 ± √(25 - 24)) / 2

Step 3: x = (5 ± √1) / 2

Step 4: x = (5 ± 1) / 2

Solutions: x = 3 or x = 2