(x-2)(x-4)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-2)(x-4) = 0

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

Applying the Zero Product Property

1. Set each factor equal to zero:

   • (x - 2) = 0
   • (x - 4) = 0

2. Solve for x in each equation:

   • x = 2
   • x = 4

Solutions

Therefore, the solutions to the equation (x-2)(x-4) = 0 are x = 2 and x = 4. These are the values of x that make the equation true.

Interpretation

This equation represents a parabola that intersects the x-axis at two points: x = 2 and x = 4. These points are the roots or solutions of the equation.

Key Takeaways

• The Zero Product Property is a powerful tool for solving factored quadratic equations.
• By setting each factor equal to zero, we can find the values of x that make the equation true.
• The solutions represent the x-intercepts of the parabola represented by the equation.