Which of the following is an example of quadratic equation?

Correct answer:

x(x - 5) = x -2


x2 - 6x = x2 + 8

, Not Selected

x3 + 2x2 = 3

, Not Selected



A quadratic equation is defined as a polynomial equation of degree 2, meaning the highest exponent of the variable is 2. Let's analyze each of the given equations:

1. **\(x(x - 5) = x - 2\)**  
   Expanding the left-hand side:  
   \(x^2 - 5x = x - 2\)  
   Rearranging all terms to one side:  
   \(x^2 - 6x + 2 = 0\)  
   This is a quadratic equation because the highest power of \(x\) is 2.

2. **\(x^2 - 6x = x^2 + 8\)**  
   Subtracting \(x^2\) from both sides:  
   \(-6x = 8\)  
   This is a linear equation (degree 1), **not** a quadratic equation.

3. **\(x^3 + 2x^2 = 3\)**  
   This is a cubic equation because the highest power of \(x\) is 3, **not** a quadratic equation.

Therefore, the **correct answer** is:

**\(x(x - 5) = x - 2\)**, as it simplifies to a quadratic equation.

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Would you like more details on how to solve this quadratic equation or any specific part of the process?

Here are 5 related questions to expand on this topic:

1. How do you solve a quadratic equation by factoring?
2. What is the quadratic formula, and when should you use it?
3. How do you determine if a quadratic equation has real or complex solutions?
4. What are the properties of the graph of a quadratic equation?
5. Can a quadratic equation have more than two real solutions?

**Tip**: Always check the degree of the equation first to determine if it is quadratic, cubic, or linear.

Which of the following is an example of quadratic equation?
Correct answer: x(x - 5) = x - 2
x^2 - 6x = x^2 + 8, Not Selected
x^3 + 2x^2 = 3, Not Selected

Learn how to identify quadratic equations by analyzing the degree of the polynomial. This problem explains how to recognize and solve quadratic equations, such as x(x - 5) = x - 2, and compares it with other equations of different degrees. Suitable for students in Grades 7-9.

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