Complex Numbers And Quadratic Equations question 537
Question: The quadratic in $ t $ , such that A.M. of its roots is $ A $ and G.M. is G, is [IIT 1968, 1974]
Options:
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
Show Answer
Answer:
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 $ .
BETA
