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

Question 977119: find the root of the polynomial p(x)=x^4 + 4x^3 +6x^2 + 4x + 5 = 0 given that one of the roots is x = -i
Found 2 solutions by josgarithmetic, anand429:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
About a week ago, answered.

Divide p(x) by or . The next two roots will be easy to identify.
Answer by anand429(138) (Show Source): You can put this solution on YOUR website!
Given

Since x= -i is one of the roots,
i.e
so is a factor (since imaginary roots occur in conjugate pairs, hence x=i is also a factor, hence this conclusion)
So arranging the equation to get above factor common, we get,

=>
So we will find the roots of using quadratic roots formula,
and
i.e and
So, the roots are i, -i, -2+i and -2-i
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