Quadratic Formula

The quadratic formula!

The quadratic formula is a powerful tool for solving quadratic equations of the form:

ax^2 + bx + c = 0

where a, b, and c are constants, and x is the variable. The formula is:

x = (-b ± √(b^2 - 4ac)) / 2a

Let’s break it down:

• a is the coefficient of the x^2 term
• b is the coefficient of the x term
• c is the constant term
• ± (plus-minus) indicates that there are two possible solutions for x
• √ (square root) is the square root of the expression inside the parentheses

To use the quadratic formula, simply plug in the values of a, b, and c into the formula, and simplify the expression.

Here’s an example:

Solve the equation: x^2 + 5x + 6 = 0

Using the quadratic formula:

x = (-5 ± √(5^2 - 4(1)(6))) / 2(1) x = (-5 ± √(25 - 24)) / 2 x = (-5 ± √1) / 2 x = (-5 ± 1) / 2

Simplifying, we get:

x = (-5 + 1) / 2 = -2 x = (-5 - 1) / 2 = -3

So, the solutions to the equation are x = -2 and x = -3.

The quadratic formula is a powerful tool for solving quadratic equations, and it’s widely used in many areas of mathematics, science, and engineering.