Question 252551
Let P(x) = X^7 and Q(x) = X.
Right now the real roots of P(x) = 0.
P(Q(x)) = X^7
Q(P(Q((x))) = x^7. 
The roots of Q(P(Q(x))) = 0.
So it appears that the degree of Q = 1.

In general, if the roots are both 0, then the degree of Q >=1, hypothesis. 
We could try to generalize this but that may take more time than what is necessary.

Hope this helps.