A company estimates its total profit (profit = total revenue minus total cost) as
P(x) = 2x^5 − 3x^4 − 5x^2 − 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.
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no not really
The rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or is less than it by an even number. Multiple roots of the same value are counted separately.
How many sign changes are there in this polynomial
P(x) = 2x^5 − 3x^4 − 5x^2 − 2
there is one sign change
P(x) = +2x^5 − 3x^4 − 5x^2 − 2
I see one sign change.