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

Jasonbradley

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Jun 17, 2024

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

This equation is a simple quadratic equation in factored form. We can solve it using the Zero Product Property, which states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Here's how to solve it:

1. Set each factor equal to zero:

   • x - 6 = 0
   • x - 2 = 0

2. Solve for x in each equation:

   • x = 6
   • x = 2

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

Understanding the Solution

The solutions, x = 6 and x = 2, represent the x-intercepts of the parabola represented by the equation. This means that the graph of the equation will cross the x-axis at the points (6, 0) and (2, 0).

Visual Representation

If you were to graph the equation y = (x-6)(x-2), you would see a parabola opening upwards, intersecting the x-axis at the points (6, 0) and (2, 0).

Conclusion

The equation (x-6)(x-2) = 0 is a simple example of a quadratic equation that can be solved using the Zero Product Property. By setting each factor equal to zero and solving for x, we find the solutions to the equation, which represent the x-intercepts of the parabola.