Question

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

Answer 1

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