What is the Quadratic Formula?
The quadratic formula is a powerful tool in algebra used to solve quadratic equations, which are equations of the form:
ax² + bx + c = 0
The Formula
The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / 2a
Where:
- a is the coefficient of x²
- b is the coefficient of x
- c is the constant term
How to Use the Quadratic Formula
To solve a quadratic equation using the quadratic formula, follow these steps:
- Identify the values of a, b, and c from the quadratic equation.
- Plug these values into the quadratic formula.
- Simplify the expression under the square root (the discriminant), b² - 4ac.
- Take the square root of the discriminant.
- Compute the two possible solutions using the ± sign.
Example
Let's solve the quadratic equation:
x² - 5x + 6 = 0
Here, a = 1, b = -5, and c = 6.
Now, substitute these values into the quadratic formula:
x = (-(-5) ± √((-5)² - 4(1)(6))) / 2(1)
Simplifying further:
x = (5 ± √(25 - 24)) / 2
Then:
x = (5 ± √1) / 2
We have two possible solutions:
x = (5 + 1) / 2 = 3 or x = (5 - 1) / 2 = 2
The solutions are x = 3 and x = 2.