<s>[INST] Polynomial of 4th degree I would like to ask if someone could help me with the following equation.
\begin{equation}
x^4+ax^3+(a+b)x^2+2bx+b=0
\end{equation}
Could you first solve in general then $a=11$ and $b=28$.
I get it to this form but I stuck.
\begin{equation}
1+a\left(\frac{1}{x}+\frac{1}{x^2}\right)+b\left(\frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^3}+\frac{1}{x^4}\right) = 0
\end{equation}
Thank you in advance.
 [/INST] You are almost there !
$$1+a\left(\frac{1}{x}+\frac{1}{x^2}\right)+b\left(\frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^3}+\frac{1}{x^4}\right) = 0$$
$$1+a\left(\frac{x+1}{x^2}\right)+b\left(\frac{x+1}{x^3}+\frac{x+1}{x^4}\right) = 0$$
$$1+a\left(\frac{x+1}{x^2}\right)+b\left(\frac{x+1}{x^2}\right)^2 = 0$$
</s>