Use the given zero to find the remaining zeros of the function.

[tex]h(x) = 7x^5 + 2x^4 + 210x^3 + 60x^2 - 1512x - 432[/tex]

Zero: [tex]-6i[/tex]

The remaining zero(s) of [tex]h[/tex] is(are): [tex]\square[/tex]

(Use a comma to separate answers as needed. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)

To find the remaining zeros of the polynomial function given one zero as [tex]\(-6i\)[/tex], we can use the property of polynomials that states complex roots occur in conjugate pairs. Therefore, if [tex]\(-6i\)[/tex] is a zero, its conjugate [tex]\(6i\)[/tex] is also a zero.

We start with the function:

[tex]\[ h(x) = 7x^5 + 2x^4 + 210x^3 + 60x^2 - 1512x - 432 \][/tex]

1. Identify Known Zeros:
The given zero is [tex]\(-6i\)[/tex]. This implies [tex]\(6i\)[/tex] is also a zero due to the conjugate pair property.

2. Search for Other Zeros:
The remaining zeros can be found by dividing the polynomial by the quadratic factor associated with the complex zeros [tex]\((-6i)\)[/tex] and [tex]\(6i\)[/tex], which is [tex]\(x^2 + 36\)[/tex].

3. Factor and Solve:
We can then factor the polynomial or use other methods to find the remaining zeros. The factorization reveals that the remaining zeros are:
- [tex]\(-\frac{2}{7}\)[/tex]
- [tex]\(-\sqrt{6}\)[/tex]
- [tex]\(\sqrt{6}\)[/tex]

4. Conclusion:
Thus, the remaining zeros of the function [tex]\(h(x)\)[/tex] are [tex]\(-\frac{2}{7}\)[/tex], [tex]\(-\sqrt{6}\)[/tex], and [tex]\(\sqrt{6}\)[/tex].

These are the additional roots, apart from the ones initially given. If you have any more questions or need further clarification, feel free to ask!