A polynomial function with rational coefficients has the follow zeros. Find all additional zeros. \( \begin{array}{l}-3+\sqrt{5},-i \\ \text { a }-3-\sqrt{5},-i \\ \text { b } 3+\sqrt{5}, i \\ \text { c }-3-\sqrt{5}, i \\ \text { d } 3-\sqrt{5},-i\end{array} \)

To find all additional zeros of the polynomial function with rational coefficients, we need to apply the Conjugate Root Theorem. This theorem states that if a polynomial has rational coefficients, then any irrational or complex roots must occur in conjugate pairs. 1. For the zero \(-3 + \sqrt{5}\), its conjugate \(-3 - \sqrt{5}\) is already given. So, we have both zeros. 2. The zero \(-i\) requires that its conjugate, \(i\), also be a zero. Thus, the complete list of zeros is: \[ -3 + \sqrt{5}, \quad -3 - \sqrt{5}, \quad -i, \quad i \] So the additional zeros are \( -3 - \sqrt{5} \) and \( i \).