Solve each problem. Use Descartes' rule of signs to determine the...

Question

Solve each problem. Use Descartes' rule of signs to determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of ƒ(x)=x^3+3x^2-4x-2.

Accepted Answer

Or the following function identify the possible number of positive negative and non real complex zeros. Using the carts rule of science where we have F of X equals to five X to the third plus nine X squared minus eight X minus seven. Not to solve this. Let's first look for the positive routes. Our rule states that the number of sign changes in our equation F of X is equivalent to the number of positive real roots. So our functions coefficients are 59 N eight and negative seven. We notice we have one sign change right in the middle going from a positive nine to a negative eight because we have one sign change. And our F of X, we have one positive real root. We can now check our negative roots to check our negative roots. We will check F of negative X and substitute negative X. And for every X, it means we get five multiplied by negative X to the third plus nine, multiplied by negative X squared minus eight, multiplied by negative X minus seven giving us now the third plus nine X squared plus eight X minus seven. Let's check the number of sign changes in our new polynomial. We have negative 598 and negative seven as our coefficients. We notice we have two sign changes, one from negative 5 to 9 and one from eight to negative seven. Because we have two sign changes, we will have either two or zero, negative real roots. You have one positive real route or two or zero, negative real roots. This means the answer to our problem is answer D OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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Solve each problem. Use Descartes' rule of signs to determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of ƒ(x)=x^3+3x^2-4x-2.