Algebra
posted by Tim
Find the polynomial function P of the lowest possible degree, having real coefficients, with the given zeros.
3+2i, 2 and 1

MathMate
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 32i is therefore
P(x)=(x(2))(x1)(x32i)(x3+2i)
=(x+2)(x1)(x²6x+13)
Expand if necessary
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