Final answer:
The question has a typo in the polynomial function, making it unclear how to proceed with finding the remaining zeros. Once the correct function is known, if 4 - 5i is a given zero, its conjugate 4 + 5i will also be zero, and we can use polynomial division and the quadratic formula to find the remaining zeros.
Step-by-step explanation:
To find the remaining zeros of the polynomial function h(x) = x^4 - 12x^3 + 28x^2 + 1962 - 1845 given one of the zeros as 4 - 5, we need to use polynomial division or synthetic division to simplify the polynomial using the given zero. However, there seems to be a typo in the provided function. Assuming the typo concerns the constant terms and should perhaps read h(x) = x^4 - 12x^3 + 28x^2 + bx - c, where b and c are constants to be determined, we would proceed as follows:
First, we know that if 4 - 5i is a zero, its complex conjugate 4 + 5i is also a zero due to the complex conjugate root theorem. We can then use these zeros to factor the polynomial. To find the remaining zeros, we would divide the polynomial by the factors corresponding to these roots and then solve the resulting quadratic equation.
If the polynomial simplifies to a quadratic form, such as ax^2 + bx + c = 0, we would use the quadratic formula to find the remaining zeros. Assuming we have correct coefficients, the quadratic formula is x = √{b^2-4ac}∗{-b ± over 2a}. Using this, we can find the remaining zeros.
Since the given polynomial does not appear to be correct, and the zeroes in the options do not seem to pertain to the provided polynomial, it is recommended to verify the polynomial function before proceeding with finding the zeros.