Answer:
Therefore, the number of possible negative zeros is 2.In summary, the given function has 1 possible positive zero and 2 possible negative zeros.
Explanation:
The number of possible positive zeros of a polynomial function is equal to the number of sign changes in its coefficients when the polynomial is written in descending order, and if one were to search for the zeros. Similarly, the number of possible negative zeros is equal to the number of sign changes in the coefficients of the function when it is written in ascending order.Using this rule for the given polynomial function:
f(x) = 3x^3 + 14x^2 + 13x - 6
The coefficients in descending order are 3, 14, 13, and -6. There is one sign change in the coefficients (from positive to negative) between 14 and 13. Therefore, the number of possible positive zeros is 1
When the coefficients are written in ascending order, they become -6, 13, 14, and 3. There are two sign changes in the coefficients (from negative to positive and then back to negative) between -6 and 13, and between 14 and 3.