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Solving the Equation (x+4)(x-2)=0
The equation (x+4)(x-2) = 0 is a simple quadratic equation that can be solved using 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 the equation:
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Set each factor equal to zero:
- x + 4 = 0
- x - 2 = 0
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Solve for x in each equation:
- x = -4
- x = 2
Therefore, the solutions to the equation (x+4)(x-2) = 0 are x = -4 and x = 2.
Understanding the Zero Product Property
The Zero Product Property is a fundamental concept in algebra. It allows us to solve equations where we have a product of factors equal to zero. By setting each factor equal to zero, we can find the individual values of the variable that make the entire equation true.
Visualizing the Solutions
We can visualize the solutions of this equation by plotting the graph of the quadratic function represented by the equation. The graph will intersect the x-axis at the points where the function equals zero. In this case, the graph intersects the x-axis at x = -4 and x = 2. These points represent the solutions to the equation.
Conclusion
The equation (x+4)(x-2) = 0 is a simple example of how the Zero Product Property can be used to solve quadratic equations. By understanding this property, we can easily find the solutions to such equations and gain a deeper understanding of the relationship between factors and roots in algebra.