(x-1)-0.jpeg "(x-9)(x-1) 0")
Solving the Equation (x - 9)(x - 1) = 0
This equation is a simple quadratic equation, and we can solve it using the Zero Product Property. This property states that if the product of two or more 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 - 9)(x - 1) = 0
This means either:
- (x - 9) = 0 or
- (x - 1) = 0
Now, we can solve for x in each case:
-
x - 9 = 0
- Adding 9 to both sides, we get x = 9
-
x - 1 = 0
- Adding 1 to both sides, we get x = 1
Therefore, the solutions to the equation (x - 9)(x - 1) = 0 are x = 9 and x = 1.
Understanding the Solution
These solutions represent the x-intercepts of the parabola defined by the equation y = (x - 9)(x - 1). This means that the graph of the parabola crosses the x-axis at the points (9, 0) and (1, 0).
In summary, we used the Zero Product Property to quickly solve the quadratic equation and find its roots, which are the x-values where the equation equals zero.