If the roots of the cubic equation are in G.P., then
Step-1: Determine the sum and product of roots of the given equation
Let are the roots of the given equation
Since are in G.P.
Let be the common ratio, the roots are as
Substituting the above in equations (1), (2), and (3).
Step-2: Solve equations (4), (5), and (6) for a, b, and c.
Divide equation (4) by (5)
Step-3: Put in equation (6)
Therefore, option (1) is the correct option.