which I cannot do :P
Well, I just dont remember the best method to answer it
"
show that the equation has only one real root."
Thanks a lot
By Descartes rule of signs it has at most 1 positive real root.
Also changing the sign of all odd power terms and applying Descartes rule of signs agrain we see that it has at most 0 negative real roots.
But this is a cubic and so has at leat one real root, and so it must have exactly one real root and its positive.
RonL