Q1. If a, b, c are in G.P., then the equations ax2 + 2 points
2bx + c = 0 and dx2 + 2ex + f = 0 have a
common root if d/a, elb, f/c are in
O O
(a) AP
O O
(b) GP
O O (C) HP
0 (
(d) none of these
Answers
Answered by
1
Answer:
Hence, d/a,e/b and f/c are in A.P
Ans (a) AP
Step-by-step explanation:
Consider ax²+2bx+c=0
As a,b and c are in G.P., let b=ar and c=ar²
then the above becomes ax²+2arx+ar²=0
or a(x²+2rx+r²)=0
i.e. a(x+r)²=0 and hence x=−r is the only root of ax²+2bx+c=0.
i.e. −r is also the root of dx²+2ex+f=0
So dr²−2er + f=0
dividing this by ar² we get
d/a−2er/ar²+f/ar²=0
or d/a-(2e)/ar + f/c=0 (as b=ar and c=ar²)
d/a-(2e)/b + f/c=0
or d/a − e/b =e/b−f/c
Hence, d/a,e/b and f/c are in A.P
Ans (a) AP
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