Question 7 of 10 , Step 1 of 1 Correct Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros. Be sure to include all possibilities. \[ g(x)=9 x^{12}+3 x^{10}+6 x^{8}+7 x^{6}+7 \] Answer How to enter your answer (opens in new window) Separate multiple answers with commas. Number of Positive Real Zeros: Number of Negative Real Zeros:

Step 1 ：Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros. The rule states that the number of positive real zeros of a polynomial is equal to the number of sign changes between consecutive non-zero coefficients, or less than that by an even number. The number of negative real zeros is found by applying the rule to the polynomial obtained by replacing x by -x.

Step 2 ：In this case, the polynomial is \(g(x)=9 x^{12}+3 x^{10}+6 x^{8}+7 x^{6}+7\). We can see that there are no sign changes in the coefficients, so there are no positive real zeros.

Step 3 ：To find the number of negative real zeros, we replace x by -x to get \(g(-x)=9 (-x)^{12}+3 (-x)^{10}+6 (-x)^{8}+7 (-x)^{6}+7\). Simplifying this gives \(g(-x)=9 x^{12}+3 x^{10}+6 x^{8}+7 x^{6}+7\), which is the same as the original polynomial. Therefore, there are also no negative real zeros.

Step 4 ：Final Answer: The number of positive real zeros is \(\boxed{0}\) and the number of negative real zeros is also \(\boxed{0}\).