Will these teeth need to be extracted? (Photo)

Hello. Of course we can't see xray and so have no idea about periapical tissues. But probably a root canal treatment and filling or crown can be done to save the tooth

To address your inquiry, we kindly request you to upload your X-ray panoramic film here. To determine the appropriate treatment approach, advanced radiological imaging (tomography) and clinical examination are necessary.

While the photo doesn't look great, and might even be very uncomfortable, the tooth may be restorable. Without an xray and exam, it is just a guess. Its likely that in order to save the tooth, root canal therapy and a crown would be needed.