The set of solutions to the inequality $x ^ { 2 } + b x + c < 0$ is the interval $p < x < q$ where $b , c , p$ and $q$ are real constants with $c < 0$.
In terms of $p , q$ and $c$, what is the set of solutions to the inequality $x ^ { 2 } + b c x + c ^ { 3 } < 0$ ?
A $\frac { p } { c } < x < \frac { q } { c }$
B $\frac { q } { c } < x < \frac { p } { c }$
C $p c < x < q c$
D $q c < x < p c$
E $p c ^ { 2 } < x < q c ^ { 2 }$
F $q c ^ { 2 } < x < p c ^ { 2 }$