SOLUTION: How do I find a polynomial function with rational coefficients so that P(x)=0 has the given roots: 13i and 5 + 10i. I tried this: P(x)=(x+13i)(x^2 + 5 + 10) but when I multipl

Question 493151: How do I find a polynomial function with rational coefficients so that P(x)=0 has the given roots: 13i and 5 + 10i.
I tried this:
P(x)=(x+13i)(x^2 + 5 + 10) but when I multiply everything out it is Way off from the answer in the back of the book.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
complex roots (those containing i) occur in conjugate pairs (a+bi and a-bi)
___ also; if r is a root, then x-r is a factor

so P(x) has four factors ___ (x + 13i)(x - 13i)[x - (5 + 10i)][x - (5 - 10i)]

multiplying the factors should give you the right result
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