(x%2B5)%3D0.jpeg "(x-5)(x+5)=0")
Solving the Equation (x-5)(x+5) = 0
This equation is a simple quadratic equation that can be solved using the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.
Let's break down the solution:
- Identify the factors: In this case, the factors are (x-5) and (x+5).
- Apply the Zero Product Property: For the product of these factors to equal zero, at least one of them must be zero. So, we have two possibilities:
- (x-5) = 0 or
- (x+5) = 0
- Solve for x:
- For (x-5) = 0, add 5 to both sides to get x = 5.
- For (x+5) = 0, subtract 5 from both sides to get x = -5.
Therefore, the solutions to the equation (x-5)(x+5) = 0 are x = 5 and x = -5.
Understanding the Concept
This equation represents a parabola that intersects the x-axis at two points, x = 5 and x = -5. These points are called the roots or zeros of the equation. They are the values of x that make the equation true.
Visual Representation
You can visualize this solution by graphing the function y = (x-5)(x+5). The graph will be a parabola that crosses the x-axis at x = 5 and x = -5.
Conclusion
By applying the Zero Product Property, we can efficiently solve quadratic equations in factored form. This principle is fundamental in algebra and helps us understand the relationships between factors, roots, and graphs of polynomial functions.