Math CentralQuandaries & Queries


Question from Krys, a student:

How do I find a polynomial P(x) with integer coefficient that has degree 4 and zeroes 1-2i and 1 (with multiplicity of 2)?

Hi Krys,

You need two facts to solve this problem. First if a is a zero of a polynomial then (x - a) is a factor, and if a is a zero of a polynomial of multiplicity k then (x - a)k is a factor. The second fact is that if the polynomial has real coefficients and a + bi is a zero then its complex conjugate a + bi is also a zero.


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