Question in complex numbers from GRE This is a question motivated from GRE subgect test exam.
if f(x) over the real number has the complex numbers $2+i$ and $1-i$ as roots,then f(x) could be:
a) $x^4+6x^3+10$
b) $x^4+7x^2+10$
c) $x^3-x^2+4x+1$
 d) $x^3+5x^2+4x+1$
 e) $x^4-6x^3+15x^2-18x+10$
What I thought at first was to calculate $(x-2-i)(x-1+i)$ and find the polynomial that is divisible by it.Unfortunately it turns out that $(x-2-i)(x-1+i)$ is complex polynomial which makes thing harder to calculate and since this is a multiple choice question with very limited time there must be an easier way. Then I thought maybe it will be easy if I write the complex numbers in polar form and check explicitly if they are the roots.But I don't think that's a very efficient way as well. Then I noticed that the question ends with "$f(x)$ could be" which may suggest that there is a way eliminate the wrong choices, however I have no idea what to eliminate or not.
Does anyone have any ideas?
Thanks in advance

1. 
$(x-(2-i))(x-(2+i))$
$x^2-x(2+i)-x(2-i)+(2-i)(2+i)$
$x^2-2x-xi-2x+xi+(4-2i+2i+1)$
$x^2-4x+5$
2. 
$(x-(1-i))(x-(1+i))$
$x^2-x(1+i)-x(1-i)+(1-i)(1+i)$
$x^2-x-xi-x+xi+(1+i-i+1)$
$x^2-2x+2$
3.
$(x^2-4x+5)(x^2-2x+2)$
$x^4-2x^3+2x^2-4x^3+8x^2-8x+5x^2-10x+10$
$x^4-6x^3+15x^2-18x+10$
