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# Find a polynomial function of the lowest degree w/real coefficients that has the following zeros: -5, 2, 1+3i?

Please show me how to do this as ive never done one where i haven't been given the degree.

Update:

i know, but for some reason after that it's not coming out right..i would then multiply the (x+5) by (x-2) and seperately multipy the 1+3i equations, right?

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- 9 years agoFavorite Answer
If it has real coefficients and a complex root, another root must be the conjugate of that root. Therefore the four roots (solutions) are -5, 2, 1+3i and 1-3i. You then get a polynomial in factorised form of (x-(-5))(x-2)(x-(1+3i))(x-(1-3i)) you can then expand these to get the polynomial.

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