If the roots of the equation `(b-c)x^2+(c-a)x+(a-b)=0` are equal then `a,b,c` will be in

Explanation

Give equation is
`a(b-c)x^(2)+b(c-a)x+c(a-b)=0`…………i
Here, coefficient of `x^(2)+` coefficient of `x+` constant term `=0`
i.e. `a(b-c)+b(c-a)+c(a-b)=0`
The, 1 is a root of Eq. (i)
Since, its roots are equal.
Therefore its other root will be also equal to 1.
Then product of roots `=1xx1=(c(a-b))/(a(b-c))`
`impliesab-ac=ca-bc`
`:.b=(2ac)/(a+c)`
Hence a,b,c are in HP.