If two roots of the equation $(a-1)(x^2+x+1)^2-(a+1)(x^4+x^2+1)=0$ are real and distinct, then find the interval in which $a$ lies.
I have expanded the equation to obtain a quartic equation which I am not able to factorize: $$ x^4+(1-a)x^3+(2-a)x^2-ax+1=0 $$
If only I could factorize it I would get two quadratic equations, one of which should have real roots. I know how to proceed further in order to find the interval in which a lies.
But as for now I don't know how to proceed further. It would be great if I could get a hint to move forward.