Posted by Jill on Tuesday, July 26, 2011 at 9:57am.
complex roots always come in pairs, so if 2-i is a root, so is 2+i
using the sum and product of roots property of a quadratic,
sum of roots = 2-1 + 2+i = 4
product or roots = (2-i)(2+i) = 4 - i^2 = 5
so the quadratic part would be
x^2 - 4x + 5
the other factor would be x-2
so the polynomial is
(x-2)(x^2 - 4x + 5)
I will leave it up to you to expand it, if you need it in that form.
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