SOLUTION: Write a polynomial function with rational coeffecients so that P(x)=0 has the given roots. i and 5i

Question 390322: Write a polynomial function with rational coeffecients so that P(x)=0 has the given roots.
i and 5i
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
By Vieta's formulas, the sum of the roots is real, so the sum of the other roots must be C - 6i for real C. There are actually infinitely many polynomials satisfying this.

We know the polynomial must be in the form

where Q(x) is a polynomial with complex coefficients. If we let two roots of Q(x) be -5i and -i, then the polynomial will have real coefficients. Therefore we can let where R(x) has real coefficients.

where R(x) is a polynomial with real coefficients. I'm sure many other solutions exist, but the problem only asks for one polynomial.
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