Question

# If both the roots of a(b−c)x2+b(c−a)x+c(a−b)=0 are equal, then a,b,c are in

A
A.P.
B
G.P.
C
H.P.
D
None of these

Solution

## The correct option is C H.P.a(b−c)x2+b(c−a)x+c(a−b)=0 By observation, sum of coefficient =0, so x=1 is one root of the equation, So both of the roots are 1, Product of roots c(a−b)a(b−c)=1⇒ac−bc=ab−ac⇒2ac=ab+bc⇒b=2aca+c Therefore, a,b,c are in H.P.

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