An entrepreneur estimates his total profit (total revenue minus total cost) for his proposed company as p(x) = x3 − 4x2 + 5x − 2
0, where p is in hundreds of dollars and x is number of years the company has been in business. In which year (x) will the entrepreneur break even? a)year 1
b)year 2
c)year 3
d)year 4
To "break even" means that the costs are equal to the money made, so profit would have to be 0. Therefore, we can rewrite the equation to be 0 = x3 -4x2 +5x -20
From here, all you have to do is factor to be able to solve for the values of x
First, since the first two numbers both have an x2, we can factor that out x2(x-4) + 5x -20 = 0
The next two can factor out a 5 x2(x-4) + 5(x-4) =0
Since both of these terms share an (x-4), they can be factored to become: (x-4) (x2 +5) = 0
So now we just solve for x, and get x = 4, and +- (sqrt) 5i
Since 4 is the only answer present in the options (and since 5i is a non-real number), the answer would be 4
