This is (Almost Certainly) a Rhetorical Question
You likely know that already, but since this is a site for learners at all levels of fluency, I’ll go into this with some examples.
At minimum, you want to be aware of this figure of speech so you don’t sound like you’re asking a rhetorical question when you don’t mean to.
"But, dad, didn't you promise me a new laptop?"
The adverb not makes this a rhetorical question. That is, his father did in fact promise his son Rajeev a laptop, and the son remembers. Phrasing it as a question is a polite way to remind the father of his promise, without directly contradicting him. This is reinforced by the word “But,” which implies that this is a response to a statement Rajeev disagrees with.
In American English, I would ask, “Did you promise me a laptop?” if I were genuinely unsure whether he had or had not. The adverb not in the main verb of a question almost always means that the expected answer is yes.
A good example of this construction is the song “It’s over, isn’t it? Isn’t it? Isn’t it over? You won, and she chose you, and now she’s gone.” The speaker is asking the same thing three different ways, but already knows the answer. (Here, asking as a question represents her denial of something she knows to be true.)
To ask a rhetorical question where the expected answer is no, add a positive question tag at the end, such as “is it?” “did he?” or “have you?”
So, “Dad. did you promise me a laptop?” is usually a plain question, and the most likely way for Rajeev to ask his father to clarify or confirm it. “You didn’t promise me a laptop, did you?” is a rhetorical question with the opposite implication, that Rajeev doesn’t think that’s what his father really meant.
In modern English, such rhetorical questions almost always use contractions, and asking one without using a contraction is very formal or old-fashioned. You see the word not written out in rhetorical questions in some translations of the Bible. (“Is this not so?” when the answer is supposed to be yes, or “This is not so, is it?” when the answer is supposed to be no.) Otherwise, “did you not?” or “is it not?” sounds like something an arrogant lawyer might ask a witness on cross-examination.
Your Textbook Gave Bad Advice
I respectfully have to disagree with the answer it gives, and I hope that’s not representative of the quality of the book.
Rajeev reminded his dad if he hadn't promised him a new laptop.
First, at least where I live, you never “*remind someone if ....” That usage is incorrect. You can “ask someone if ...” or “ask someone whether ...” but you “remind someone that ...” or “remind someone how ....” It’s one of those arbitrary rules that don’t get written down anywhere, and are so hard for non-native speakers to memorize. I don’t have a name for it and can’t explain why that is, but I could immediately tell that the sentence was not written by a native speaker. On behalf of my ancestors, I apologize. A good way to check for these, though, is a ngram search on Google Books.
The suggested response seems to mash together two possible correct responses. Rajeev might “ask his father whether he hadn’t promised him a new laptop.” The same kind of rhetorical inversion works there too: “whether he had” implies it was a genuine question, but “whether he hadn’t” correctly implies that the question was rhetorical. Rajeev might also “remind his father that he had promised him a new laptop.” This just sees through the rhetorical question and summarizes it as equivalent to a direct statement.
But remember, this kind of inversion does not apply to “reminded that,” only to “asked if.” Rajeev reminded is father that he had promised. Reminding his father that he hadn’t would mean the exact opposite.
I would probably summarize a negative rhetorical question using an adverb like really. So, “Dad, you didn’t just promise me a new laptop, did you?” would become something like, “Rajeev asked his father whether he had really promised him a new laptop.” A parallel to the reminded version might be, “Rajeev doubted that his father had promised him a new laptop.”
The use of pronouns, “if he hadn’t promised him,” is ambiguous as well. This textbook was probably written for students who would assume that fathers sometimes promise to buy their sons laptops and forget, not the other way around. But if it is not clear from context which of the two men is “he” and which is “him,” you would want to say something like “his father had promised him” or “he had promised Rajeev.” A more formal option would be to say “the former” (in this case, the first person mentioned in the sentence, Rajeev) and “the latter,” (the most recent person mentioned, in this case, Rajeev’s father).