A) \[0<\alpha <\beta \]
B) \[\alpha <0<\beta <\,|\alpha |\]
C) \[\alpha <\beta <0\]
D) \[\alpha <0<\,|\alpha |\,<\beta \]
Correct Answer: B
Solution :
Given \[\alpha < \beta , c < 0, b > 0,\] \[\therefore \,\,\,\alpha +\beta =-b<0 \,and \,\alpha \beta =c<0\] Clearly, \[\alpha \] and \[\beta \] have opposite signs and \[\alpha < \beta \] \[\therefore \,\,\,\alpha < 0 \,and \,\beta >0\,\,\,\Rightarrow \,\,\alpha <0<\beta \] Further \[\alpha +\beta <0\,\,\Rightarrow \,\,\beta <\,\,-\alpha \,\,\Rightarrow \,\,\left| \beta \right|<\,\,\left| -\alpha \right|\] \[\Rightarrow \,\,\,\beta <|\alpha |\,\,(\beta >0\Rightarrow \left| \beta \right|=\beta )\] Hence, \[\alpha < 0 < \beta < \left| \alpha \right| \]
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