IS. 3 Let $\alpha$ and $\beta$ be the two roots of the equation $x^{2}+c x+b=0$, where $c<0$ and $\alpha-\beta=1$. Find the value of $c$.
Reference: 2016 FI1.3
$$
\begin{array}{l}
\alpha \beta=b=2 ;(\alpha-\beta)^{2}=1 \\
\Rightarrow(\alpha+\beta)^{2}-4 \alpha \beta=1 \\
\Rightarrow(-c)^{2}-4 \times 2=1 \\
c=-3
\end{array}
$$