Sequence And Series Question 395
Question: If the A.M. and G.M. of roots of a quadratic equations are 8 and 5 respectively, then the quadratic equation will be
[Pb. CET 1990]
Options:
A) $ x^{2}-16x-25=0 $
B) $ x^{2}-8x+5=0 $
C) $ x^{2}-16x+25=0 $
D) $ x^{2}+16x-25=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
Given that $ A.M.=8 $ and $ G.M.=5 $ , if $ \alpha ,\ \beta $ are roots of quadratic equation, then quadratic equation is $ x^{2}-x(\alpha +\beta )+\alpha \beta =0 $ ……(i) $ A.M.=\frac{\alpha +\beta }{2}=8 $
$ \Rightarrow $ $ \alpha +\beta =16 $ ……(ii) and $ G.M.=\sqrt{\alpha \beta }=5 $
$ \Rightarrow $ $ \alpha \beta =25 $ ……(iii) So the required quadratic equation will be $ x^{2}-16x+25=0 $ .
BETA
