Question

What loci are represented by the equation :
$x^3-x^2-x+1=0.$

Answer 1

$x^3-x^2-x+1=0x^2(x-1)-1(x-1)=0(x^2-1)(x-1)=0(x+1)(x-1)(x-1)=0$

So the equation represents three straight line two of which are coincident.