Posted by Tim on Thursday, March 10, 2011 at 5:29pm.
The zeroes of polynomials are either real or complex. Complex zeroes always come in with the conjugates.
Since the three zeroes above do not include conjugates, the minimum degree of polynomial is 3+1=4.
The polynomial having zeroes of
3+2i, -2, 1
and the conjugate 3-2i is therefore
P(x)=(x-(-2))(x-1)(x-3-2i)(x-3+2i)
=(x+2)(x-1)(x²-6x+13)
Expand if necessary
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