An entrepreneur estimates that the total profit (profit = total revenue minus total cost) from his proposed company will be given by the function P(x) = x3 – 4x2 + 3x – 12, where P is in hundreds of dollars and x is the number of years elapsed after the company starts operations. In how many years (x) will the company break even (no profit, no loss)? 1 year

Accepted Solution

No profit means P(x)=0: x³-4x²+3x-12=0
factor by regrouping: x²(x-4)+3(x-4)=0
take out (x-4): (x-4)(x²+3)=0
x=4 or x²=-3
x² is not a negative number, so x=4 is the only answer.