Answer: 1 or zero
Step-by-step explanation:
To determine the possible number of positive and negative real zeros of the function f(x) = 8x^6 + 9x^3 + 1, we can use Descartes’ Rule of Signs.
First, we count the number of sign changes in the coefficients of the polynomial. In this case, there are two sign changes from 8 to 9 and from 9 to 1. This means that there are either 2 or 0 positive real zeros.
Next, we find f(-x) and count the number of sign changes in the coefficients of the resulting polynomial. In this case, f(-x) = -8x^6 + 9x^3 + 1, which has one sign change from -8 to 9. This means that there is either 1 or 0 negative real zeros.
Therefore, the possible number of positive real zeros of f(x) is 2 or 0, and the possible number of negative real zeros is 1 or 0.
