If the ratio of the roots of x² + bx + c = 0 is equal to the ratio of the roots of x² + px + q = 0, then p²c–b²q =

If the ratio of the roots of $a{x}^2+bx+c=0$ is $m:n$ then ${\left(m+n\right)}^{2}ac=mn{b}^2$

Given that the ratio of roots of $x^2+bx+c=0$ is equal to the ratio of the roots of $x^2+px+q=0$ then

${\left(m+n\right)}^{2}c=mn{b}^2$ and ${\left(m+n\right)}^{2}q=mn{p}^2$

it implies that 

$\frac{c}{q}=\frac{b^2}{p^2}\Rightarrow p^{2}c=b^{2}q$

Therefore,  $p^{2}c-b^{2}q=\boxed{0}$