(x-8)(x-2)=0

2 min read Jun 17, 2024

Solving the Equation (x-8)(x-2) = 0

This equation represents a simple quadratic equation in factored form. To solve for the values of 'x' that satisfy the equation, we can utilize the Zero Product Property.

Understanding the Zero Product Property

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Applying the Property

In our equation, (x-8) and (x-2) are the two factors. Therefore, for the product to be zero, either:

x - 8 = 0
- Solving for x, we get x = 8
x - 2 = 0
- Solving for x, we get x = 2

Solution

Therefore, the solutions to the equation (x-8)(x-2) = 0 are x = 8 and x = 2. These are the two values of 'x' that make the equation true.

Graphical Representation

This equation represents a parabola that intersects the x-axis at the points (8, 0) and (2, 0). These points correspond to the solutions we found.

Conclusion

By applying the Zero Product Property, we can easily solve factored quadratic equations like (x-8)(x-2) = 0. The solutions represent the x-intercepts of the corresponding parabola.