The correct answer is A. would not be.
The sentence “Unless I have a quiet room I would not be successful” is in the present tense. It is a conditional sentence, which means that it expresses a condition that must be met in order for the result to occur. In this case, the condition is that the speaker must have a quiet room in order to be successful. The result is that the speaker will not be successful if they do not have a quiet room.
The other options are incorrect because they are not in the present tense. Option B, “shall not be,” is in the future tense. Option C, “have not been,” is in the past tense. Option D, “had not been,” is in the past perfect tense.
In conclusion, the correct answer to the question “Unless I have a quiet room I . . . . . . . . successful” is A. would not be.