The set [tex]\{x\mid x^4-x^3-x^2-6x+6=0\}[/tex] is the set of all values of [tex]x[/tex] that are solutions to the given equation. So all you need to do is check whether [tex]x=1[/tex] and [tex]x=2[/tex] satisfy the equation.
[tex]x=1\implies 1^4-1^3-1^2-5+6=0[/tex]
[tex]x=2\implies2^4-2^3-2^2-10+6=0[/tex]
The equation holds, so both 1 and 2 are solutions, and hence [tex]\{1,2\}[/tex] is a subset of the solutions.
