Show that the equation $x^n=f(x)$ where $f(x)$ is a polynomial with positive coefficients of degree $n-1$, has only one positive root.
I found this problem but I'm having trouble solving it and I would really like some help.
I thought proof by contradiction by assuming that we have at least two positive roots that satisfy the equation but I don't really know where to go from there.
Sorry for any mistakes in my English. It's not my native language