A polynomial function with rational coefficients has the follow zeros. Find all additional zeros, \( -1+i, \sqrt{5} \) \( \begin{array}{l}\text { a } \\ \text { b }-1-i \\ \text { c }-1-i,-\sqrt{5} \\ \text { d } 1-1-i\end{array} \) \( \begin{array}{l}5\end{array} \)

When you have a polynomial with rational coefficients, any complex zeros must occur in conjugate pairs. Since one of your zeros is \(-1+i\), its conjugate \(-1-i\) must also be a zero. Similarly, since \(\sqrt{5}\) is a zero, its negative counterpart \(-\sqrt{5}\) must also be included as a zero. Thus, the complete list of zeros should include: \(-1+i\), \(-1-i\), \(\sqrt{5}\), and \(-\sqrt{5}\). So the answer is **\( -1-i, -\sqrt{5} \)**, which corresponds to option **c**. Now you can confidently tackle polynomials, knowing that their complex and irrational zeros come with partners, bringing harmony to their otherwise unpredictable natures!