Math, asked by yomgesora, 5 months ago

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 Anonymous
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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