Posted by Anonymous on Friday, May 7, 2010 at 7:47pm.
well, if one root is -i, it has another root +i, as complex roots will appear in conjugates. (x+i)(x-i)=(x^2+1) is a factor. So, divide that into the polynomial....
(x^4-5x^3+7x^2-5x+6)/(x^2+1)=
x^2-5x+6=(x-3)(x-2)
so the roots are i, -i, 3,2
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