$p(x) =x^6 + ax^5+ bx^4 +x^3 + bx^2 + ax + 1$ Given that p(1)=0 but p(-1) is not zero. What is maximum number of distinct real roots of p(x)?
I divided by $x^3$ and made a cubic in t, where $t=x+1/x$, but after that what can i say? My cubic is $t ^3+ at^2 + (b-3)t + 1-2a=0$ where t= 2 is one root, which gives repetation of x=1. now the cubic has a quadratic factor. how can i comment on nature of root of quadratic?
is it right to say that quad can maximum give 2 that means in x i have four so , max is 5?