G4.2 Let $\alpha, \beta$ be the roots of $x^{2}+b x-2=0$. If $\alpha>1$ and $\beta<-1$, and $b$ is an integer, find the value of $b$.
$\begin{array}{l}\alpha-1>0 \text { and } \beta+1<0 \\ \Rightarrow(\alpha-1)(\beta+1)<0 \\ \Rightarrow \alpha \beta+\alpha-\beta-1<0 \\ \Rightarrow \alpha-\beta<3 \\ \Rightarrow(\alpha-\beta)^{2}<9 \\ \Rightarrow(\alpha+\beta)^{2}-4 \alpha \beta<9 \\ \Rightarrow b^{2}+8<9 \\ \Rightarrow-1<b<1 \\ \because b \text { is an integer } \\ \therefore b=0\end{array}$