Sequence And Series Question 306
Question: If A is the A.M. of the roots of the equation $ x^{2}-2ax+b=0 $ and $ G $ is the G.M. of the roots of the equation $ x^{2}-2bx+a^{2}=0, $ then
[UPSEAT 2001]
Options:
A) $ A>G $
B) $ A\ne G $
C) $ A=G $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Sum of the roots of $ x^{2}-2ax+b^{2}=0 $ is 2a, Therefore, A = A.M. of the roots = a. Product of the roots of $ x^{2}-2bx+a^{2}=0is,a^{2} $ Therefore, G.M. of the roots is $ G=a $ Thus, $ A=G $
BETA
