A) \[\frac{2}{3}\]
B) \[-\frac{2}{3}\]
C) \[\frac{1}{3}\]
D) \[-\frac{1}{3}\]
Correct Answer: A
Solution :
Let the roots are a and 2a Þ \[\alpha +2\alpha =\frac{1-3a}{{{a}^{2}}-5a+3}\] and \[\,\alpha .2\alpha =\frac{2}{{{a}^{2}}-5a+3}\] Þ \[2\left[ \frac{1}{9}\frac{{{(1-3a)}^{2}}}{{{({{a}^{2}}-5a+3)}^{2}}} \right]=\frac{2}{{{a}^{2}}-5a+3}\] Þ \[\frac{{{(1-3a)}^{2}}}{({{a}^{2}}-5a+3)}=9\]\[\Rightarrow 9{{a}^{2}}-6a+1=9{{a}^{2}}-45a+27\] Þ \[39a=26\]\[\Rightarrow a=\frac{2}{3}\].
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