Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form.
3i, 2 - i

Step-by-step explanation:

The idea here is probably that 3i and 2 -i are zeros of the desired polynomial.   Since the coefficients are rational, the complex zeros come in complex conjugate pairs.  This means that  -3i and  2+ i are also zeros.  A start on the polynomial is to write

  P(x) = (x - 3i) (x + 3i) (x -(2-i) )( x - (2 +i))

  Multiplying this all out results in

 P(x) =  x4  + 14 x2  + 45

Since the coefficient of the leading term is 1,   this is the final answer.  

step-by-step explanation:

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