Understanding the Components of a Quadratic Equation: Identifying A, B, and C in x2 - 8x - 2 0

Introduction to Quadratic Equations

Quadratic equations are fundamental in algebra and are used extensively in various fields of mathematics and science. A quadratic equation is an equation of the form:

ax2 bx c 0

where x is the variable, and a, b, and c are constants, with a ≠ 0.

Identifying the Coefficients in a Quadratic Equation

Given a quadratic equation in the form:

x2 - 8x - 2 0

we can identify the coefficients a, b, and c as follows:

Step-by-Step Process

Compare the given equation with the standard form ax2 bx c 0.

Determine the value of a, which is the coefficient of the term with x2. In this case, a 1.

Identify the coefficient of the term with x. Here, it is -8, so b -8.

Recognize the constant term, which is the term without any x. In the given equation, c -2.

Example and Explanation

Let's look at the example of the quadratic equation x2 - 8x - 2 0. Here are the values of the coefficients:

a 1

Since the coefficient of the x2 term is 1, it is understood that a 1.

b -8

The coefficient of the x term is -8, so b -8.

c -2

The constant term, which is the term without x, is -2, so c -2.

Conclusion

Understanding how to identify the coefficients a, b, and c in a quadratic equation is crucial for solving and manipulating algebraic expressions. By following the steps outlined above, you can easily determine the values of these coefficients in any given quadratic equation. This knowledge forms the basis for solving more complex algebraic problems.