Option D is Correct.
Let the roots of the equation be alpha and beta.
sum of the roots of the quadratic equation ax 2 + bx + c = 0 is equal to the sum of the squares of their reciprocals.
α + β = (1/α2 ) + (1/β2) = (α2 + β2) / (α*β)2 = ((α + β)2 - 2α*β) / (α*β)2
Therefore, Put Sum of roots = - (b/a) and Product of roots is c/a in ((α + β)2 - 2α*β) / (α*β)2
-(b/a) = ( b2 / a2 - 2*(c/a) ) / (c/a)2 ...... (Sum of roots = - (b/a) and Product of roots is c/a ....Acc to Vieta's formula for quadratic equation)
-(b/a) = ( b2 / c2 ) - 2a/c
2(a2)*c = a(b2) + b(c2) ............(Divide the equation by abc)
2a/b = b/c +c/a
c/a , a/b and b/c are in AP
So a/c, b/a and c/b are in HP.