Using the Descartes Rule of Sign count the number of sign changes of f(x) and determine the number of positive real zeros.
1. f(x)=x^3+x^2-10x-24
My answer: because the signs don't change the answer would be: "0 sign changes of f(x), which means f(x) has 0 positive real zeros".
1 sign change, so there is exactly 1 positive real root.
The sign change is from +x^2 to -10x
Thank you Steve for your response. I appreciate it very much.
To use the Descartes' Rule of Signs, you need to follow these steps:
1. Write down the equation of the function f(x). In this case, f(x) = x^3 + x^2 - 10x - 24.
2. Count the number of sign changes in the coefficients of f(x). Starting from the leftmost coefficient, count every time the sign changes. In this case, we have the following coefficients: +1, +1, -10, -24. There are two sign changes (from +1 to +1 and from -10 to -24).
3. The number of sign changes can give you an upper limit for the number of positive real zeros. In this case, since there are two sign changes, there can be at most 2 positive real zeros.
It is important to note that the number of sign changes only gives an upper limit, not an exact count of positive real zeros. To find the exact count, you may need to use other techniques such as factoring, synthetic division, or graphing the function. In this case, you have correctly determined there are no sign changes and therefore, according to Descartes' Rule of Signs, there are 0 positive real zeros.