2. Given the integer coefficient equation about $x$
$$
x^{2}+(k+3) x+(2 k+3)=0
$$

has one positive root and one negative root, and the absolute value of the positive root is less than the absolute value of the negative root. Then the positive root of the equation is $\qquad$
2. $\frac{-1+\sqrt{5}}{2}$.

From the conditions, we get
$$
\begin{array}{l}
\left\{\begin{array}{l}
(k+3)^{2}-4(2 k+3)>0, \\
2 k+3=x_{1} x_{2}0
\end{array}\right. \\
\Rightarrow k \in\left(-3,-\frac{3}{2}\right) .
\end{array}
$$

Thus, the integer value of $k$ is -2. At this point, the equation is $x^{2}+x-1=0$, and the positive root is $\frac{-1+\sqrt{5}}{2}$.