A) \[{{t}^{2}}-2At+{{G}^{2}}=0\]
B) \[{{t}^{2}}-2At-{{G}^{2}}=0\]
C) \[{{t}^{2}}+2At+{{G}^{2}}=0\]
D) None of these
Correct Answer: A
Solution :
If \[\alpha ,\beta \] are the roots, then \[A=\frac{\alpha +\beta }{2}\]Þ\[\alpha +\beta =2A\]and\[G=\sqrt{\alpha \beta }\,\,\,\Rightarrow \alpha \beta ={{G}^{2}}\] The required equation is\[{{t}^{2}}-2At+{{G}^{2}}=0\].
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