A) \[0<\alpha <\beta \]
B) \[\alpha <0<\beta <\,|\alpha |\]
C) \[\alpha <\beta <0\]
D) \[\alpha <0<\,|\alpha |\,<\beta \]
Correct Answer: B
Solution :
Here \[D={{b}^{2}}-4c>0\] because c < 0 < b. So roots are real and unequal. Now, \[\alpha +\beta =-b<0\] and \[\alpha \beta =c<0\] \ One root is positive and the other negative, the negative root being numerically bigger. As \[\alpha <\beta ,\,\alpha \]is the negative root while b is the positive root. So, \[|\alpha |\,>\beta \,\text{and}\,\,\alpha <0<\beta .\]
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