Question

Zeros are 1,2,4i, and 3-2i. List the remaining zeros of the polynomial.

Answer 1

The remaining zeros of the polynomial, given that 1, 2, 4i, and 3-2i are zeros and following the Complex Conjugate Root Theorem, are -4i and 3+2i.

Step-by-step explanation:

Given the zeros of a polynomial are 1, 2, 4i, and 3-2i, the remaining zeros of the polynomial can be determined by the Complex Conjugate Root Theorem.

This theorem states that if a polynomial has real coefficients, then the non-real complex zeros must occur in conjugate pairs.

Thus, if 4i is a zero, its complex conjugate -4i is also a zero, and if 3-2i is a zero, its complex conjugate 3+2i is also a zero.

The remaining zeros of the polynomial are therefore -4i and 3+2i.