is a root and the coefficients are real, the second root has to be 2−i√3
=x2−4x+7 is a root of the given equation.
Dividing the original equation by x2−4x+7, we have
Thus, we obtain the other root as x2+4x+5
Again factorizing this root, we get x=−4±√16−202
The four roots are therefore 2+i√3,2−i√3,−2+i,−2−i