Toss turnips, potatoes in 1 tablespoon olive oil add marjoram,1/2 teaspoon salt and1/4 teaspoon pepper together in a medium bowl. Spread in a even layer on a large baking sheet. Roast for 15 minutes
Meanwhile, place flour in a shallow dish. Transfer 2 tablespoons of the flour to a small bowl and whisk in broth; set aside. Season chicken with the remaining 1/4 teaspoon salt and 1/4 teaspoon pepper dredge the chicken in the flour shaking off excess. Heat remaining 1 tablespoon oil in a large skillet over medium heat, add the chicken skinned side down and cook until well browned on the bottom; about five minutes remove from heat
After the vegetables have been roasting or 15 minutes stir them and place one piece of chicken skinned side up in each corner of the baking sheet(set the skillet aside) return the vegetables and chicken to the oven and roast until the chicken is cooked through and the vegetables are tender about 20 minutes more.
When the chicken and vegetables have about 10 minutes left return to the skillet to medium heat add shallots and cook stirring until fragrant about one minute risk they reserved broth mixture again , add to the pan and bring to a boil. Cook stirring occasionally until reduced by about 1/2 stir in mustard and vinegar. Serve the chicken and vegetables with the sauce