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There cannot be such a polynomial.

If a polynomial has rational coefficients, then any complex roots must come in conjugate pairs. In this case the conjugate for 2-3i is not a root. Consequently, either

(a) the function is not a polynomial, or

(b) it does not have rational coefficients, or

(c) 2 - 3i is not a root (nor any other complex number), or

(d) there are other roots that have not been mentioned.

In the last case, the polynomial could have any number of additional (unlisted) roots and is therefore indeterminate.

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Q: Which polynomial has rational coefficients a leading leading coefficient of 1 and the zeros at 2-3i and 4?
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