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Question

If the roots of equation a(bc)x2+b(ca)x+c(ab)=0 be equal. then a,b,c are in


A

A.P.

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B

H.P

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C

G.P

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D

None of these

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Solution

The correct option is B

H.P


Given Equation: a(bc)x2+b(ca)x+c(ab)=0(i)

Here the coefficient of x2+coefficient of x+constant term=0
i.e., a(bc)+b(ca)+c(ab)=0

Therefore 1 satisfies equation (i) then 1 is a root of equation(i).

Since its roots are equal.
Hence its other root will be also equal 1.

The product of the roots =c(ab)a(bc)=1;

b=2ac(a+c)

Hence a,b,c are in H.P.


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