If one roots of the equation x 2/a = x/b + 1/c = 0 is reciprocal of the other, then which one of the following is correct?

Given quadric equation is
x² + x/b + 1/c = 0 ...(i)
Now, by condition the roots of the Eq.(i) are α and 1/α.
Now,product of roots = (1/c) / (1/a)
⇒ α.(1/α) = a/c
⇒ c = a
which is the required relation.