Let $\;\alpha\;$ and $\;\beta\;$ be the roots of equation $\;px^{2} +qx + r=0\;,p \neq 0\;$ .if p ,q ,r are in A.P. and $\;\large\frac{1}{\alpha} + \large\frac{1}{\beta}=4\;$ then the value of $\;|\alpha - \beta|\;$ is :

Question

$(a)\; \large\frac{\sqrt{34}}{9} \qquad(b)\; \large\frac{ 2 \sqrt{13}}{9}\qquad(c)\; \large\frac{\sqrt{61}}{9}\qquad(d)\;\large\frac{2\sqrt{17}}{9}$