# Math Help - Polynomial Function

1. ## Polynomial Function

Hey all , I am working on the following, any comments would be appreciated.

Find a polynomial function P(x) that has zeros of -5, 3(multiplicity 2), 2 + i, and 2 - i, with degree 5.

Thanks - AC-

2. Originally Posted by AlgebraicallyChallenged
Hey all , I am working on the following, any comments would be appreciated.

Find a polynomial function P(x) that has zeros of -5, 3(multiplicity 2), 2 + i, and 2 - i, with degree 5.

Thanks - AC-
Try multiplying out

$(x+5)(x-3)^2(x-2-i)(x-2+i)=(x+5)(x-3)^2(x^2-4x+5)$

3. $x_1=-5, \ x_2=x_3=2, \ x_4=2+i, \ x_5=2-i$

$P(x)=(x-x_1)(x-x_2)(x-x_3)(x-x_4)(x-x_5)=(x+5)(x-2)^2(x^2-4x+5)$