Cut tops from beets, leaving 1-inch stems. Peel beets, and cut into quarters. Place on a 12-inch square of aluminum foil. Drizzle with 1 tablespoon olive oil; sprinkle with rosemary, 1/4 teaspoon salt, and 1/8 teaspoon pepper. Fold up foil sides, forming a bowl. Place foil bowl in 1 end of a large roasting pan; set aside.
Peel shallots; cut in half lengthwise.
Toss together shallots, carrots, potatoes, turnips, remaining 3 tablespoons oil, remaining 3/4 teaspoon salt, and remaining 1/8 teaspoon pepper. Place in remaining end of roasting pan.
Bake at 450° for 30 to 40 minutes or until tender.