the value of :$ ((a-b)(b-c)(c-a))^2$ If the polynomial : $f(x)=x^3-3x+2$ have the roots :$a,b,c$
How to find the value of :$$ ((a-b)(b-c)(c-a))^2$$

We have $f'(x) = 3x^2 - 3$, so $f'(x) = 0$ when $x = \pm 1$. We also have $f(1) = 1^3 - 3(1) + 2 = 0$, so $1$ is in fact a double root. Can you now determine the value of the desired expression?
