Question: If $x_1,x_2,x_3$ are such that $x_1+x_2+x_3=2$ , $x_1^2+x_2^2+x_3^2=6$ and $x_1^3+x_2^3+x_3^3=8$. Then find the value of $-(x_2-x_3)(x_3-x_1)(x_1-x_2)$.
My attempt: Tried to correlate the values of $x_1,x_2,x_3$ but no fruitful result yet. Idk why they look like some polynomial roots to me, but I can be wrong in this context. Please help