Solve the equation

Question:

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

  1. $\frac{\sqrt{61}}{9}$

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

  3. $\frac{\sqrt{34}}{9}$

  4. $\frac{2 \sqrt{13}}{9}$


Correct Option: , 4

Solution:

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