Final answer:
The x-intercepts of the function f(x) = 5x^2 - 25x / x are x = 0 and x = 5.
Step-by-step explanation:
The x-intercepts of a function are the values of x where the graph of the function intersects the x-axis.
To find the x-intercepts of the function f(x) = 5x^2 - 25x / x, we set f(x) equal to zero and solve for x.
5x^2 - 25x / x = 0
Since division by zero is undefined, we need to eliminate the denominator.
We can do this by multiplying both sides of the equation by x:
5x^2 - 25x = 0
Now, we can factor out the common factor of x and solve for x:
x(5x - 25) = 0
Setting each factor equal to zero gives us:
x = 0
and
5x - 25 = 0
From the second equation, we can solve for x:
5x = 25
x = 5
Therefore, the x-intercepts of the function f(x) = 5x^2 - 25x / x are x = 0 and x = 5.