SOLUTION: find the roots of the polynomial p(x) = x^4+4x^3+6x^2+4x+5=0 given that one of the roots is x= -i

Question 976056: find the roots of the polynomial
p(x) = x^4+4x^3+6x^2+4x+5=0 given that one of the roots is x= -i
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
Another root is x=i, because complex roots for polynomial functions come as conjugate pairs. Those two roots are as

, a factor of the polynomial p(x).

Use polynomial division for as dividend
and as divisor. The quotient represents the rest of the factors, as quadratic, degree two.
-
The division process not shown here; but result is as the quotient.

Use general solution method for a quadratic equation to find the zeros of this factor:
roots are

or -2-i and -2+i.

(along with -i and i ).
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