anonymous
  • anonymous
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.
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
@Nnesha
anonymous
  • anonymous
@pooja195
anonymous
  • anonymous
Do you know the Descrates rule of signs

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anonymous
  • anonymous
no not really
anonymous
  • anonymous
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.
anonymous
  • anonymous
How many sign changes are there in this polynomial P(x) = 2x^5 − 3x^4 − 5x^2 − 2
anonymous
  • anonymous
4
anonymous
  • anonymous
there is one sign change
anonymous
  • anonymous
P(x) = +2x^5 − 3x^4 − 5x^2 − 2 I see one sign change.
anonymous
  • anonymous
You there?

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