If one of the roots of the equation $px^{2} + qx + r = 0$ where $p \neq 0$ and $p, q, r \in R$ is $x = -2$,then prove that $4p - 2q + r = 0$.

(N/A) Given the quadratic equation is $px^{2} + qx + r = 0$.
Since $x = -2$ is a root of this equation,it must satisfy the equation.
Substituting $x = -2$ into the equation,we get:
$p(-2)^{2} + q(-2) + r = 0$
$p(4) - 2q + r = 0$
$4p - 2q + r = 0$
Hence,it is proved that $4p - 2q + r = 0$.