is it possible to develop an analytical solution (root) for such a polynomial: $f(x)=\left(x^{10}-c_1^2\right)\left(c_2-x\right)^2-0.2\left(x^2-1\right)c_1^2$ with $c_1$ and $c_2 >0$.
Numerical methods can help, however, the convergence speed is not as satisfactory as desired. Thanks in advance.