16(!). Determine \(p\) so that the sum of the absolute values of the roots of the equation \(z^{2}+p z-6=0\) is equal to 5.
16. Solution. Let \(x\) and \(y\) be the roots of the given equation. Since the product of the roots is -6, they have different signs. Let \(x>0\) and \(y<0\). Then, using the conditions of the problem and Vieta's theorem, we can form the following system of two equations with two unknowns:

\[
\left\{\begin{array}{l}
x y=-6 \\
x+(-y)=5
\end{array}\right.
\]

We obtain two solutions: 3 and -2 or 2 and -3. The number \(p\) will be found using the condition \(p=-(x+y)\). Answer: 1 or -1.