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| Math Central | Quandaries & Queries |
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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.
Penny
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