Heat oven to 450 degrees F. Dry chicken with paper toweling. Remove excess fat. Sprinkle with salt and pepper inside and out. Place tarragon and thyme in cavity of chicken. Slip tips of chicken wings under bird. Tie legs closely together. Place chicken, breast side down, in roasting pan large enough to hold vegetables heaped around it. Place potatoes, onions and carrots around chicken.
Roast in 450 degree F oven for 30 minutes.
Lower oven temperature to 350 degrees F. Turn chicken, breast side up. Add mushrooms around chicken in pan. Add chicken broth. Roast another 45 minutes. Insert skewer or fork into thickest part of thigh. If juices run pink or red, roast another 10 to 15 minutes. Remove chicken to platter; let rest 5 to 7 minutes before cutting into portions. Return roasting pan with vegetables to oven for another 15 minutes or until tender.