(x-3)(x-8)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-3)(x-8) = 0

This equation is a simple quadratic equation in factored form. To solve it, we can use 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.

Here's how to solve it:

1. Set each factor equal to zero:

   • x - 3 = 0
   • x - 8 = 0

2. Solve each equation for x:

   • x = 3
   • x = 8

Therefore, the solutions to the equation (x-3)(x-8) = 0 are x = 3 and x = 8.

Explanation:

The equation (x-3)(x-8) = 0 represents a parabola that intersects the x-axis at the points x = 3 and x = 8. These points are the roots or solutions of the equation. When x is equal to either 3 or 8, one of the factors becomes zero, making the entire product equal to zero.

In summary, the Zero Product Property allows us to find the solutions to factored quadratic equations by setting each factor equal to zero and solving for x.