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) ?

Question

Mathematics

Ernest

13 July, 12:44

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) ?

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Answers (1)

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Aden Blackwell · 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.