Algebra 2
posted by Anonymous .
Given that the polynomial has the given root, find all roots of the polynomial.
P(x) = x^4  5x^3 + 7x^2  5x + 6; i

well, if one root is i, it has another root +i, as complex roots will appear in conjugates. (x+i)(xi)=(x^2+1) is a factor. So, divide that into the polynomial....
(x^45x^3+7x^25x+6)/(x^2+1)=
x^25x+6=(x3)(x2)
so the roots are i, i, 3,2