How determine relationship between two $n$ degree polynomials roots

Question

Suppose we have the following polynomial equations: $$a_nx^n+a_{n-1}x^{n-1}+...a_0=0,$$ $$b_nz^n+b_{n-1}z^{n-1}+...b_0=0.$$ I need to analytically determine the relationship between $x^*$ and $z^*$ in terms of $>,<$ or $=$ signs.$x^*$ and $z^*$ are roots of the corresponding polynomial equations. In order to determine the relationship, the main problem is that we have polynomials, which are $n$-degree, where $n>5$. About coefficients is known only that $a_i\neq b_i$, for $i=1,...,n.$ Therefore, I think we need to apply unconventional techniques to solve the problem. Please guide me.

Answer 1

Use a good computer with good software to find the numerical solutions.

Otherwise, there's no easy way; the information you've given is completely insufficient to do any kind of analysis, unless we have the specific values of $a_i,b_i$.