Question

Please help me with this! show that {1,2} ⊆ {x|x^4 - x^3 - x^2 - 5x + 6 = 0}

Answer 1

The set $\{x\mid x^4-x^3-x^2-6x+6=0\}$ is the set of all values of $x$ that are solutions to the given equation. So all you need to do is check whether $x=1$ and $x=2$ satisfy the equation.

$x=1\implies 1^4-1^3-1^2-5+6=0$

$x=2\implies2^4-2^3-2^2-10+6=0$

The equation holds, so both 1 and 2 are solutions, and hence $\{1,2\}$ is a subset of the solutions.