If I want to prove $x^n+x^{n-1}-a=0$ has only one positive root for $a> 0$ and $n \ge 2$ Can I say for $n=2$ : $x^2+x-a=0$ and we know only one of the roots is positive. Now if we we know there is only one root for $x^n+x^{n-1}-a=0$ now I prove for $x^{n+1}+x^{n}-a=0$ In the end I get to $x=1$ , but I don't think I’m doing it correctly. Should I use different $a$ s?
Is my way wrong? If it is, could you tell me what I should do?