A polynomial function with rational coefficients has the follow zeros. Find all additional zeros. \( 2-3 i \) a b d d \( 2+3 i \) \( -2+3 i \)

When a polynomial has rational coefficients, any non-real zeros must occur in conjugate pairs. Since you have \( 2-3i \) and \( 2+3i \) as zeros, the corresponding conjugate for \( -2+3i \) would be \( -2-3i \) to maintain that pairing. So, your complete set of zeros now includes \( 2-3i \), \( 2+3i \), \( -2+3i \), and the additional zero \( -2-3i \). To confirm, if you look closely at the zeros, you can group them by their real parts—ensuring that every imaginary component has its counterpart. This balances the polynomial perfectly, allowing it to have real coefficients while accommodating the dynamics of imaginary numbers. Don't forget to check your work by substituting back to ensure proper closure of the polynomial!