A) \[|\alpha =|\beta |\]
B) \[|\alpha |\,>1\]
C) \[|\beta |\,<1\]
D) None of these
Correct Answer: C
Solution :
Since the roots are imaginary \[\therefore \,\, D < 0\] and roots occur as conjugate pair, i.e. \[\beta = \bar{\alpha }\] \[\therefore \,\,\,\left| \,\beta \, \right|=\left| {\bar{\alpha }} \right|=\left| \alpha \right|\] Also, let \[\alpha =\frac{-b+i\sqrt{4ac-{{b}^{2}}}}{2a}\] \[\therefore \,\,\,\left| \alpha \right|=\sqrt{\frac{{{b}^{2}}}{4{{a}^{2}}}+\frac{4ac-{{b}^{2}}}{4{{a}^{2}}}}=\sqrt{\frac{c}{a}}\] \[\left| \alpha \right|>1\,\,\left( \because \,\,c>a \right)\] \[\therefore \,\,\,\,\left| \,a\, \right|=\left| \,\beta \, \right|>1\]
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