Preheat the oven to 375 degrees F. Place the chicken on a rimmed baking pan.
In a small bowl, stir to combine the olive oil, chopped rosemary, thyme, sage, red pepper flakes, grated garlic, lemon zest, 1 tablespoon salt and 2 teaspoons black pepper. Rub the chicken all over with half of the herb oil, being sure to spread some under the skin of the breasts and thighs to season the flesh. Stuff the cavity with the rosemary, thyme and sage sprigs, the bay leaves, 1/2 lemon and garlic head halves.
Place the rutabaga, carrots and turnips in a large bowl. Toss to coat with the remaining herb oil. Scatter the vegetables around the chicken and transfer to the oven. Roast until the vegetables are tender and the chicken is cooked through, with an instant-read thermometer inserted at the thickest point of the thigh reading 160 degrees F, about 1 hour 15 minutes. Let rest 10 minutes before carving. Serve with the vegetables.