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?

Answer 1

Answer:

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