The polynom $A= (a-b)x^4+(c+d)x^3+(e-f)x^2+(g+h)x$ has the roots 0 and the roots of unity, so A is a multiplicity of $x(x^3-1)$. That means $c+d=0, e-f=0$. And one can say 4a-b=1$ and $g+h=-1$ without loss of generality. My question ist: why it is true only with w.l.o.g ?
You are given and are told that this is equal to where A= a- b. Then, obviously, c+ d= e- f= 0.
Also, g+ h= -A= -a+ b. I don't understand that "4" in "4a- b" at all. If it had said "we can take a- b= 1 and g+ h= -1" I could understand that- factor out (a- b).