A) \[(-2,\,\,1)\]
B) \[(-\infty ,\,\,-2)\cup (0,\,\,1)\]
C) \[(-2,\,\,0)\cup (1,\,\,\infty )\]
D) \[(-1,\,\,0)\cup (2,\,\,\infty )\]
Correct Answer: B
Solution :
If the points \[(\alpha ,\,\,2+\alpha )\] and \[\left( \frac{3\alpha }{2},\,\,{{\alpha }^{2}} \right)\]are on the opposite sides of\[2x+3y-6=0\],then \[(2\alpha +6+3\alpha -6)(3\alpha +3{{\alpha }^{2}}-6)<0\] \[\Rightarrow \] \[15({{\alpha }^{2}}+\alpha -2)<0\] \[\Rightarrow \] \[\alpha (\alpha +2)(\alpha -1)<0\] \[\Rightarrow \] \[\alpha \in (-\infty ,\,\,-2)\cup (0,\,\,1)\]You need to login to perform this action.
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