(x-1)-0.jpeg "(x-6)(x-1) 0")
Solving the Equation (x-6)(x-1) = 0
This equation represents a quadratic expression set equal to zero. To solve for the values of x that satisfy this equation, we can utilize 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.
Let's break down the equation:
- (x-6)(x-1) = 0
We have two factors: (x-6) and (x-1). To make the product equal to zero, either one or both of these factors must equal zero.
Therefore, we have two possible scenarios:
Scenario 1:
- x - 6 = 0
- x = 6
Scenario 2:
- x - 1 = 0
- x = 1
Solution:
The solutions to the equation (x-6)(x-1) = 0 are x = 6 and x = 1.
In conclusion, by applying the Zero Product Property, we have successfully found the values of x that make the equation true. These values are the roots of the quadratic equation, which represent the x-intercepts of the parabola that the equation represents.