If the roots of equation a(b−c)x2+b(c−a)x+c(a−b)=0 be equal. then a,b,c are in
Given Equation: a(b−c)x2+b(c−a)x+c(a−b)=0⋯(i)
Here the coefficient of x2+coefficient of x+constant term=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(a−b)a(b−c)=1;
Hence a,b,c are in H.P.