Answer
$\left\{\pm1,\pm3\right\}$
Work Step by Step
Using factoring of trinomials, the given equation, $
p^4-10p^2+9=0
$, is equivalent to
\begin{align*}
(p^2-1)(p^2-9)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property) and solving for the variable, then
\begin{array}{l|r}
p^2-1=0 & p^2-9=0
\\
p^2=1 & p^2=9
\\
p=\pm\sqrt{1} & p=\pm\sqrt{9}
\\
p=\pm1 & p=\pm3
.\end{array}
Hence, the solution set of the equation $
p^4-10p^2+9=0
$ is $
\left\{\pm1,\pm3\right\}
$.
