**Core Concept**
The question is testing the knowledge of dental trauma and the treatment of a specific type of tooth discoloration, known as internal resorption or root resorption, often associated with traumatic injuries to the tooth. The bluish-black discoloration and radiolucent area at the apex of the tooth are characteristic findings.

**Why the Correct Answer is Right**
The correct answer involves the treatment of a non-vital tooth with a root fracture or internal resorption. The treatment should aim to preserve the tooth, but in this case, it is likely that the tooth is beyond salvation. The presence of a radiolucent area at the apex suggests a root fracture or internal resorption, which often requires extraction. **Option C** is the correct treatment approach, which involves extraction of the tooth to prevent further complications.

**Why Each Wrong Option is Incorrect**
* **Option A:** Pulpotomy or pulpectomy may be considered for non-vital teeth, but in this case, the presence of a root fracture or internal resorption makes these treatments less effective.
* **Option B:** Orthodontic treatment is not indicated for a tooth with a root fracture or internal resorption, as it may exacerbate the damage.

**Clinical Pearl / High-Yield Fact**
In cases of dental trauma, it is essential to evaluate the tooth for signs of root fracture or internal resorption, as these conditions can lead to tooth loss if not addressed promptly.

**Correct Answer:** C. Extraction of the tooth.