1.1. The curve with equation

$y=3{x}^{2}+2px+4q$

where $p$ and $q$ are non-zero constants does not meet the $x$-axis.

Show that 

{p}^{2}</p><p style="line-height: 1.7" class="text-lg tracking-wide font-normal leading-relaxed">where \(k is a constant to be found.

1.2. Given that the curve

$y=3{x}^{2}+2px+4q$

passes through the points with coordinates $(-2,6)$ and $(2,6)$, find the values of $p$ and $q$.