if a(b-c)x^2+b(c-a)x+c(a-b)=0 have equal roots then a,b,c are in----? a)A.P. b)G.P. c)H.P. d)none of

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Expert Question: if a(b-c)x^2+b(c-a)x+c(a-b)=0 have equal roots then a,b,c are in----? a)A.P. b)G.P. c)H.P. d)none o

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7 Jan 2010 17:54:44 IST

Subject: if a(b-c)x^2+b(c-a)x+c(a-b)=0 have equal roots then a,b,c are in----? a)A.P. b)G.P. c)H.P. d)no

sayantan chowdhury (0)

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if a(b-c)x^2+b(c-a)x+c(a-b)=0 have equal roots then a,b,c are in----?a)A.P. b)G.P. c)H.P. d)none of these

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7 Jan 2010 18:14:47 IST

Subject: if a(b-c)x^2+b(c-a)x+c(a-b)=0 have equal roots then a,b,c are in----?a)A.P. b)G.P. c)H.P. d)none

Akshay (1466)

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Olaaa!! Perrrfect answer.

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Observe that x=1 is a root of this equation since ab-ac+bc-ab+ac-bc = 0

if the equation has equal roots, then c(a-b)/a(b-c) = 1

c(a-b) = ab-ac

ac-bc = ab-ac

2ac = ab+bc

b=2ac/(a+c)

i.e. a,b,c are HP

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