Let α and β be the roots of equation px2+ qx+ r = 0 p≠0 If p ,q and r, n AP and 1α+1β=4 then the  value of |α−β| is

# Let $\alpha$ and $\beta$ be the roots of equation px2+ qx+ r = 0 $p\ne 0$ If p ,q and r, n AP and $\frac{1}{\alpha }+\frac{1}{\beta }=4$ then the  value of $|\alpha -\beta |$ is

1. A

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

2. B

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

3. C

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

4. D

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

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### Solution:

Given $\alpha$and $\beta$ are roots of px2 + qx + r =0, $\mathrm{p}\ne 0$
…………………….(i)
Since, p, q and r are in AP
……………………………………….(ii)

On putting the value of qin Eq. (ii), we get

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