<s>[INST] Roots of Polynomial Equation? 
$y=1/x$ so I plugged in $x=1/y$ into the equation above and got $y^{4}+y^{3}+y^{2}/c+y/4-1/2$, but apparently it's wrong, when I looked up the answer below.

What am I missing? 
 [/INST] $$\begin{align}
x^4 + x^3 + cx^2 + 4x - 2 & = 0 \\
\left(\frac{1}{y}\right)^4 + \left(\frac{1}{y}\right)^3 + c\left(\frac{1}{y}\right)^2 + 4\left(\frac{1}{y}\right) - 2 & = 0 \\
\frac{1}{y^4} + \frac{1}{y^3} + c\frac{1}{y^2} + 4\frac{1}{y} - 2 & = 0 \\
\text{multiply by }y^4\text{ since y=0 isn't a solution} \\
1 + y + cy^2 + 4y^3 - 2y^4 & = 0 \\
\text{multiply by -1 and rearrange to get the same answer as the book}
\end{align}$$
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