SOLUTION: I tried solving the following problem, but my answer didn't match up with the one at the back of the book. The problem asks me to find a polynomial function with integer coeff. tha

Question 59537This question is from textbook
: I tried solving the following problem, but my answer didn't match up with the one at the back of the book. The problem asks me to find a polynomial function with integer coeff. that has the given zeros: 0, 3,3+i, 3-i. The answer at the back of the book is x^4-9x^3+28x^2-30x. This question is from textbook

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The factor would be
(x - 0)(x - 3)(x - 3 - i)(x - 3 + i)
(x - 3 - i)(x - 3 + i) = x^2 -6x + 10
(x - 3)(x^2 - 6x + 10) = x^3 - 9x^2 + 28x - 30
(x - 0)(x^3 - 9x^2 + 28x - 30) = x^4 - 9x^3 + 28x^2 - 30x
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