If $p,q,r$ are positive and are in A.P the roots of quadratic equations $px^2+qx+r =0$ are all real for

Question

$\begin{array}{1 1} \bigg|\frac{r}{p}-7 \bigg| \leq 4 \sqrt 3 \\ \bigg|\frac{p}{r}-7 \bigg| < 4\sqrt 3 \\ all \;p\;and\;r \\ no\;p\;and\;r \end{array}$