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.Solve for the number of times the total profit become exactly zero. Hint: Use Descartes's rule of signs.

Answer 1

   Using the Descartes` rule of signs, we have to recognize how many times the signs change from positive to negative, or from negative to positive from one term to the next. There is only 1 change of signs: from +2 x5  to -3 x4. So we have only 1 real zero.
   Answer: There is only one time that the total profit become exactly zero.