a/ \(\left(x-1\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+2=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)

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b/ \(\left(x-1\right)\left(x+2\right)< 0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1< 0\\x+2>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1>0\\x+2< 0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 1\\x>-2\end{matrix}\right.\\\left\{{}\begin{matrix}x>1\\x< -2\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}1>x>-2\\x\in\varnothing\end{matrix}\right.\)

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c/ \(\left(x-1\right)\left(x+2\right)>0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\\x+2>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\\x+2< 0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>1\\x>-2\end{matrix}\right.\\\left\{{}\begin{matrix}x< 1\\x< -2\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x\in\varnothing\\-2< x< 1\end{matrix}\right.\)

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