A) \[5\sqrt{10}\]
B) \[3\sqrt{10}\]
C) \[2\sqrt{10}\]
D) None of these
Correct Answer: A
Solution :
Let roots area, b so, \[\frac{\alpha }{\beta }=\frac{2}{3}\Rightarrow \alpha =\frac{2\beta }{3}\] \ \[\alpha +\beta =\frac{m}{12}\] Þ \[\frac{2\beta }{3}+\beta =\frac{m}{12}\Rightarrow \frac{5\beta }{3}=\frac{m}{12}\] ?..(i) and \[\alpha \beta =\frac{5}{12}\Rightarrow \frac{2\beta }{3}.\beta =\frac{5}{12}\,\,\Rightarrow {{\beta }^{2}}=\frac{5}{8}\] \[\Rightarrow \beta =\sqrt{5/8}\] Put the value of b in (i), \[\frac{5}{3}.\sqrt{\frac{5}{8}}=\frac{m}{12}\]Þ \[m=5\sqrt{10}\].
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