# Polynom deg 5, coefficents are real numbers for zeroes 3, -5i, and -5+i. Identify the zeroes. A. -5i, 5-i B. 5i, -5-i C. 5i, -5+i D. -3, 5i, -5-i

If a 5 degree polinom (which has 5 roots) has real coefficients and one real zero (3) and four complex zeros, it can be written in the form

`P(x) = A(x-3)(X^2+Bx+C)(X^2+Dx+E)`

where `P_1(x) =X^2+Bx+C` and `P_2(x)=X^2+Dx+E` both have complex conjugate roots. Thus in the problem since `-5i` and `-5+i` are not complex conjugated it means each are a root of `P_1(x)` and `P_2(x)` . Therefore the other two roots that are missing are their complex conjugate `+5i` and `-5-i` .

The correct answer is B) `+5i` and `-5-i`

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