Question 986624
<pre>
Since 2 is written twice, I assume you mean the polynomial is to have
2 twice as a zero, or of multiplicity 2.

Conjugates of surds and complex numbers are also zeros:

{{{x=1+sqrt(3)i}}}, {{{x=1-sqrt(3)i}}}, {{{x=2}}}, {{{x=2}}}, {{{x=-1-sqrt(2)}}}, {{{x=-1+sqrt(2)}}}

{{{x-1-sqrt(3)i=0}}}, {{{x-1+sqrt(3)i=0}}}, {{{x-2=0}}}, {{{x-2=0}}}, {{{x+1+sqrt(2)=0}}}, {{{x+1-sqrt(2)=0}}}

{{{(x-1-sqrt(3)i)(x-1+sqrt(3))(x-2)(x-2)(x+1+sqrt(2))(x+1-sqrt(2))=0}}}

Multiply all that out.  Takes a long time:

{{{x^6-4x^5+3x^4+14x^3-48x^2+56x-16=0}}}

So polynomial that has those zeros is

{{{f(x)=x^6-4x^5+3x^4+14x^3-48x^2+56x-16}}}

Edwin</pre>