SOLUTION: write a polynomial function with rational coefficients so that it has roots (-2, 1+3i )

Question 709832: write a polynomial function with rational coefficients so that it has roots (-2, 1+3i )
Answer by josgarithmetic(39628) (Show Source): You can put this solution on YOUR website!
You seem to be asking for polynomial function with roots: -2,and 1+3i, AND 1-3i. Complex roots come as conjugate pairs.

-2 is a root:
((-2)-(k))=0
-2-k=0
-k=2
k=-2
The binomial factor is (x-(-2))=

1+3i is a root:
(1+3i-k)=0
1+3i-k=0
-k=-1-3i
The binomial factor is (x-(-1-3i))
or equal to

1-3i is a root:
(1-3i-k)=0
-k=-1+3i
k=1-3i
The binomial factor is

A satisfying function can come from

Do the multiplications, at least for the factors containing the complex numbers:
... The finished polynomial function may be:
and you could do the rest of the multiplying if needed.
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