A polynomial function with rational coefficients has the follow zeros. Find all additional zeros. \( -5, i \) Blank \( 1: \)

When dealing with polynomial functions that have rational coefficients, the presence of complex zeros means that they must occur in conjugate pairs. Since \( i \) (the imaginary unit) is a zero, its conjugate \( -i \) must also be a zero of the polynomial. Therefore, along with the given zero of \( -5 \), the additional zeros would be \( -5, i, -i \). For a complete polynomial, you can express it using its zeros. The polynomial can be formed as \( (x + 5)(x - i)(x + i) \). When you simplify that, you'll see the richness of polynomial roots at play! So keep track of those complex conjugates in your mathematical journeys!