\documentclass{standalone}
\pagestyle{empty}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}
\fill[yellow!20] (-5,-5) rectangle (5,5);
\draw [ultra thin, dashed] (-5,0)--(5,0);
\draw [ultra thin,dashed] (0,-5)--(0,5);

\draw[thick, domain=.2:5,scale=1, smooth] plot function{1/x} ;
\fill[cyan!10, domain=.2:5,scale=1, smooth] plot function{1/x}--(5,5);

\draw[thick, domain=-.2:-5,scale=1, smooth] plot function{1/x} ;
\fill [lime!20, domain=-.2:-5,scale=1, smooth] plot function{1/x}--(-5,-5) ;


\node at (4,.7) {$\alpha+\beta+\alpha\beta l=0$};
\node at (-4,-.7) {$\alpha+\beta+\alpha\beta l=0$};
\node at (3,3) {\rotatebox{-45}{no negative eigenvalues}};
\node at (-3,-3) {\rotatebox{-45}{two negative eigenvalues}};
\node at (0,0) {\rotatebox{-45}{\Large{one negative eigenvalue}}};

\end{tikzpicture}
\end{document}
