With Finesse. Your dentist or oral surgeon has the experience to tease these root tips out using specialized instruments designed to apply the forces necessary,
Extactions. Bummer that you lost those teeth. Sufficient anesthetic and special tools that will elevate the remaining roots. Before they are removed, make sure some sort of replacement is fabricated in order no have something to replace those you lost. Healing takes awhile before permanent restorations are considered.
Speak with DDS. An oral surgeon or general dentist can extract your teeth successfully. The key is to have a treatment plan. How are you going to replace the missing teeth. If implants are an option, check with the dentist prior to the extractions, re protocol. Are bone grafts/membranes to be utilized to preserve the bone? When can the implants be placed and what type of prosthesis will be fabricated?
Broken teeth. Teeth fractured at the gum line are a little more challenging to extract than whole teeth. A periodontist or an oral surgeon or a dentist with experience in extractions can do the extraction under local anesthesia or under sedation or both.