Question

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)?

Answer 1

P ( x ) = x³ - 4 x² + 3 x - 12 = 
= x² ( x - 4 ) +3 ( x - 4 ) = ( x - 4 ) · ( x² + 3 ) 
x - 4 = 0,  x = 4
x² + 3 = 0,  x² = - 3 ( there is no real solution )
Answer: In 4 years the company will break even.