a. \(\left\{{}\begin{matrix}x_1+x_2=\dfrac{7}{2}>0\\x_1x_2=\dfrac{3}{2}>0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x_1>0\\x_2>0\end{matrix}\right.\)
b. \(\left\{{}\begin{matrix}x_1+x_2=-\dfrac{7}{3}< 0\\x_1x_2=\dfrac{1}{3}>0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x_1< 0\\x_2< 0\end{matrix}\right.\)
c. \(\left\{{}\begin{matrix}x_1+x_2=-\dfrac{3}{5}< 0\\x_1x_2=\dfrac{1}{5}>0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x_1< 0\\x_2< 0\end{matrix}\right.\)
d. \(\left\{{}\begin{matrix}x_1+x_2=\dfrac{2}{3}>0\\x_1x_2=\dfrac{1}{9}>0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x_1>0\\x_2>0\end{matrix}\right.\)
