(x-7)(x-2)%3D0.jpeg "(x+1)(x-7)(x-2)=0")
Solving the Equation (x+1)(x-7)(x-2)=0
This equation is a cubic equation, meaning it has a highest power of 3. To solve it, we can use the Zero Product Property. This property states that if the product of several factors is equal to zero, then at least one of the factors must be equal to zero.
Let's apply this to our equation:
(x+1)(x-7)(x-2) = 0
This means that at least one of the following must be true:
- x + 1 = 0
- x - 7 = 0
- x - 2 = 0
Now, we can solve each of these equations individually:
- x + 1 = 0 => x = -1
- x - 7 = 0 => x = 7
- x - 2 = 0 => x = 2
Therefore, the solutions to the equation (x+1)(x-7)(x-2) = 0 are:
x = -1, x = 7, and x = 2
These solutions represent the x-intercepts of the graph of the cubic function represented by the equation.
Understanding the Equation
The given equation represents a cubic function which is a polynomial function with the highest degree of 3. The factored form of the equation helps us understand the behavior of the function and its intercepts.
- (x + 1) represents a factor that contributes to a root at x = -1.
- (x - 7) represents a factor that contributes to a root at x = 7.
- (x - 2) represents a factor that contributes to a root at x = 2.
These roots, also known as zeros, are the points where the function crosses the x-axis.
Conclusion
Solving the equation (x+1)(x-7)(x-2) = 0 involves applying the Zero Product Property to find the individual roots of the equation. The solutions represent the x-intercepts of the cubic function represented by the equation. Understanding the factored form helps us analyze the behavior and key features of the function.