What does Descartes rule of signs say about number of positive real roots and negative real roots of P (x) x^3+6x^2+9x+5

Question

Dylan Zhang

Mathematics

21 January, 19:24

What does Descartes rule of signs say about number of positive real roots and negative real roots of P (x) x^3+6x^2+9x+5

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Answers (1)

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Taylor Montgomery · Answer 1

There are no positive roots

Step-by-step explanation:

The Descartes' rule posits that, given a polynomial with real coefficients ordered, the number of positive roots is equal to the amount of sign-changes OR to such amount minus a number multiple of 2. In you polynomial P (x) = x^3+6x^2+9x+5 you have NO sign-changes, as every coefficient is positive. So, we can confirm that, if the polynomial has real roots, none of these are positive. As 0 can'y be a root of P (x) (replace x=0 and confirm), if there is some root, it will be a negative root. However, the rule can't confirm that there are roots.