A) \[\frac{\sqrt{61}}{9}\]
B) \[\frac{2\sqrt{17}}{9}\]
C) \[\frac{\sqrt{34}}{9}\]
D) \[\frac{2\sqrt{13}}{9}\]
Correct Answer: D
Solution :
\[\frac{1}{\alpha }+\frac{1}{\beta }=4\] |
\[2q=P+r\] |
\[\Rightarrow \] \[-2(\alpha +\beta )=1+\alpha \beta \] |
\[\Rightarrow \] \[2-\left( \frac{1}{\alpha }+\frac{1}{\beta } \right)=\frac{1}{a\beta }+1\] |
\[\Rightarrow \] \[\frac{1}{\alpha \beta }=-9\] |
Equation having roots \[\alpha ,\beta \] |
\[9{{x}^{2}}+4x-1=0\] |
\[\alpha ,\beta =\frac{-4\pm \sqrt{16+36}}{2\times 9}\] |
\[\left| \alpha -\beta \right|=\frac{2\sqrt{3}}{9}.\] |
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