find a polynomial of lowest degree with only real coefficients and having the given zeros.
1+2i, 2 (multiplicity 2)

Jordan,

If a number a is a zero of a polynomial then (x - a) is a factor of the polynomial. If a is a root of multiplicity k then (x - a)^{k} is a factor of the polynomial. The other fact you need is that if a polynomial with real coefficients has a complex zero then the complex conjugate is a zero also. Thus in your situation both 1 + 2i and 1 - 2i are zeros of the polynomial.

Does this help?

Penny

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