Answer:
Step-by-step explanation:
The function f(x) = 27x^6 + 26x^3 - 1 is a polynomial of degree 6. To determine the number of possible positive and negative real zeros of the function, we can use Descartes’ Rule of Signs.
First, we count the number of sign changes in the coefficients of the polynomial. There are two sign changes, from positive to negative and from negative to positive. Therefore, there are either 2 or 0 positive real zeros.
Next, we count the number of sign changes in the coefficients of the polynomial when we substitute -x for x. There is only one sign change, from negative to positive. Therefore, there is exactly one negative real zero.
Thus, the number of possible positive real zeros of the function f(x) = 27x^6 + 26x^3 - 1 is 2 or 0, and the number of possible negative real zeros is 1
