(x-2)(x-6)=0

2 min read Jun 17, 2024

Solving the Equation (x-2)(x-6) = 0

This equation is a simple quadratic equation in factored form. To find the solutions, we can utilize the Zero Product Property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.

Applying the Zero Product Property

Set each factor equal to zero:
- (x - 2) = 0
- (x - 6) = 0
Solve for x in each equation:
- x - 2 = 0 => x = 2
- x - 6 = 0 => x = 6

The Solutions

Therefore, the solutions to the equation (x-2)(x-6) = 0 are x = 2 and x = 6.

Understanding the Concept

This equation represents a parabola that intersects the x-axis at two points: x = 2 and x = 6. These points are the roots or solutions of the equation.

Further Exploration

You can further explore quadratic equations by:

Graphing the equation: This will visually represent the solutions as the points where the parabola intersects the x-axis.
Expanding the equation: You can multiply out the factors to get the standard quadratic form: ax² + bx + c = 0.
Using the quadratic formula: This formula can be used to solve any quadratic equation, regardless of whether it's factored or not.