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. identify the year (x) the entrepreneur will break even.

a. year 1
b. year 2
c. year 3
d. year 4

break even means that the total income is equal to the total cost.

Therefore, we can equal the total gain to zero.

We have then:

Equaling zero we have:

Rewriting the polynomial we have:

We observe that the polynomial only has a real solution.

Therefore we have:

the year (x) the entrepreneur will break even is:

D. year 4