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?

Year in which the entrepreneur break even is 4

Step-by-step explanation:

We are given:

p (x) = x^3-4x^2+5x-20

We would find the value of x

Solving:

x^3-4x^2+5x-20 = 0

(x^3-4x^2) + (5x-20) = 0

x^2 (x-4) + 5 (x-4) = 0

(x-4) (x^2+5) = 0

=> x-4 = 0 and x^2+5 = 0

x = 4 and x^2 = - 5

x = 4 and x = ±√-5 or ±√5 i (not real solutions)

So, x = 4

So, year in which the entrepreneur break even is 4