Mathematics

Problem

Let

\alpha, \beta

be the roots of the equation

px^2 + qx + r = 0

p \neq 0

. If

p, q, r

are in AP and

\frac{1}{\alpha} + \frac{1}{\beta} = 4

, the value of

|\alpha - \beta|

is a.

\frac{\sqrt{34}}{9}

\frac{2\sqrt{13}}{9}

\frac{\sqrt{61}}{9}

\frac{2\sqrt{17}}{9}