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Question

If a,b,c,x are real numbers and (a2+b2)x22b(a+c)x+(b2+c2)=0 has real & equal roots, then a,b,c are in

A
A.P
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B
G.P
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C
H.P
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D
Noneofthese
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Solution

The correct option is D G.P
Since (a2+b2)x22b(a+c)x+(b2+c2)=0 has real & equal roots.
4b2(a2+c2+2ac)4(a2+b2)(b2+c2)=0
4b2a2+4b2c2+8acb24a2b24a2c24b24b2c2=0
8acb24a2c2+4b4=0
(2ac2b2)2=0
ac=b2

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