Question

A company estimates its total profit (profit = total revenue minus total cost) as P(x) = 2x5 − 3x4 − 5x2 − 2, where P is in thousands of dollars and x is the number of years elapsed since the company was founded. How many times can the total profit become exactly zero? Hint: Use Descartes's rule of signs.

A.
2 or 0

B.
5 or 3 or 1

C.
3 or 1

D.
1

Answer 1

D. 1

Explanation:

The signs of the terms are +---, so there is 1 change of sign. That means there is 1 positive real root. Profit is zero exactly one time.