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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}+\frac{1}{\beta}$$=4$,then the value of $\mid\alpha-\beta\mid$ is

$\begin{array}{1 1}(A)\;\large\frac{\sqrt{61}}{9}\\(B)\;\large\frac{2\sqrt{17}}{9}\\(C)\;\large\frac{\sqrt{34}}{9}\\(D)\;\large\frac{2\sqrt{13}}{9}\end{array} $

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The value of $\mid\alpha-\beta\mid$ is $\large\frac{2\sqrt{13}}{9}$
Hence (D) is the correct answer.
answered Apr 7, 2014 by sreemathi.v

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