Answer
$z=-2$ and $z=2$.
Work Step by Step
The given polynomial is
$\Rightarrow z^2-4=0$
Write the the polynomial as $a^2-b^2$.
$\Rightarrow z^2-2^2=0$
Use difference of two square pattern
$a^2-b^2=(a+b)(a-b)$.
We have $a=z$ and $b=2$.
$\Rightarrow (z+2)(z-2)=0$.
Use zero product property.
$\Rightarrow z+2=0$ or $z-2=0$.
Solve for $z$.
$\Rightarrow z=-2$ or $z=2$
Hence, the solutions are $z=-2$ and $z=2$.
