Question

An entrepreneur estimates his total profit (total revenue minus total cost) for his proposed company as p(x) = x3 − 4x2 + 5x − 20, 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

Answer 1

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

ANS: D

Hope this helped ^-^

Answer 2

The correct answer is

Year 4

:)