Answer
$p=\{ \pm i, \pm2 \}$
Work Step by Step
Expressing the equation $
p^4-3p^2-4=0
$ in factored form and then using the Zero Product Property result to
\begin{array}{l}
(p^2+1)(p^2-4)=0
\\\\
p^2+1=0
\\\\
p^2=-1
\\\\
p=\pm\sqrt{-1}
\\\\
p=\pm i
,\\\\\text{OR}\\\\
p^2-4=0
\\\\
p^2=4
\\\\
p=\pm\sqrt{4}
\\\\
p=\pm2
\end{array}
Hence, the solution set is $
p=\{ \pm i, \pm2 \}
$.
