2.43 For what value of $p$ is the ratio of the roots of the equation $x^{2}+p x-16=0$ equal to -4?
2.43 We have $x^{2}+p x-16=0$ and $\frac{x_{1}}{x_{2}}=-4$. From the system $\left\{\begin{array}{l}x_{1} x_{2}=-16, \\ \frac{x_{1}}{x_{2}}=-4\end{array}\right.$

we find $x_{1}=8, x_{2}=-2$ or $x_{1}=-8, x_{2}=2$. Next, using the equality $x_{1}+x_{2}=-p$, we get $p_{1}=-6, p_{2}=6$.

Answer: for $p= \pm 6$.