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Question

If a, b c are in HP then the expression a(bc)x2 + b(c-a)x + c(a-b)


A

has real and distinct factors

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B

is a perfect square

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C

has no real factor

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D

None of these

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Solution

The correct option is B

is a perfect square


As a(b-c)+b(c-a)+c(a-b)=0, x = 1 is a root of the corresponding equation. The other root of the equation =c(ab)a(bc)=1 because, a, b, c in HP implies 1b1a=1c1b, i.e., aba=bcc
x=1, 1 are the roots of the corresponding equation. So, (x1)2 is a factor.


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