(x-7)(x+1)(x-9)=0

Jasonbradley

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Jun 17, 2024

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Solving the Cubic Equation: (x-7)(x+1)(x-9) = 0

This equation represents a cubic function, meaning it has a highest power of x of 3. Let's break down how to find the solutions (also known as roots or zeros) of this equation.

Understanding the Zero Product Property

The key to solving this equation lies in 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.

Applying the Zero Product Property

1. Identify the factors: The equation is already factored for us: (x-7)(x+1)(x-9) = 0

2. Set each factor equal to zero:

   • x - 7 = 0
   • x + 1 = 0
   • x - 9 = 0

3. Solve for x:

   • x = 7
   • x = -1
   • x = 9

Conclusion

Therefore, the solutions to the equation (x-7)(x+1)(x-9) = 0 are x = 7, x = -1, and x = 9. These are the points where the cubic function crosses the x-axis.