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?

Accepted Solution

Answer:Year in which the entrepreneur break even is 4Step-by-step explanation:We are given:p(x) = x^3-4x^2+5x-20We would find the value of x Solving:x^3-4x^2+5x-20 = 0(x^3-4x^2)+(5x-20) = 0x^2(x-4)+5(x-4) = 0(x-4)(x^2+5)=0=> x-4 = 0 and x^2+5 =0x = 4 and x^2 = -5x = 4 and x = ±√-5 or ±√5 i (not real solutions)So, x = 4So, year in which the entrepreneur break even is 4