Given, cubic equation is x3−42x2+336x−512=0 ⇒ x2(x−2)−40x(x−2)+256(x−2)=0 ⇒ (x−2)(x2−40x+256)=0 ⇒ (x−2){x2−32x−8x+256}=0 ⇒(x−2){x(x−32)−8(x−32)}=0 ⇒ (x−2)(x−32)(x−8)=0 ⇒ (x−2)(x−8)(x−32)=0 ⇒ x=2,8,32 Which represents a geometric progression in increasing order. Common ratio =