Providing an answer for your own question

Question

Usually when I post a question on Math SE, I like to provide the work that I have contributed to the problem. This is so that people don't think I am simply stating my question and assuming there will be people that spend their time writing a long and detailed answer. I recently asked a question which I intended to post my own solution to.

Notice: I posted the question in case it helped someone figure out a similar problem or inspired someone to solve a similar problem.

However, since I was going to answer my own question, I did not provide any insight into the solution in my question. Unfortunately, while I was writing my answer, the question became ill-received.

When I make questions I intend to answer in the future, how should I structure them to make it look like I am putting work into the question so it can be better received in the future?

Here is a link to the question in mind: Question

Answer 1

I think it's rather simple: write the question as if you didn't intend to self-answer it, and write the answer as if you hadn't been the one to ask the question. The question is going to be held up to the same standards as all the other questions and should stand up on its own, and similarly for your answer. Trying to cut corners will only result in disappointment.

This doesn't mean that you should artificially include "work done" (e.g. posting half the solution in the question and half in the answer) as a half-assed attempt at providing context. It's now generally accepted that "work done" is not exactly the best form of "context". There are several other, better ways. Also note that "I'm going to self-answer that question" is not context, even though some people might be more lenient in this case (wrongly, IMO).

Instead, consider this: you obviously care enough about that particular question to want to share it and its answer: why? If you can answer that, then include that as context and the world will be a better place. If you can't, you need to rethink long and hard about why you want to post that self-answered question.

Answer 2

I'd suggest you read the following post at the main Meta.Stack Exchange:

What can be done to improve moderation of self-answered questions?

There are some very helpful suggestions in the answers there, including that you "role-play" as asker and answerer. Also, don't forget that the question has to be high-quality too: when people plan to post a self-answer, there's often a temptation to be "lazy" when posting the question and omit material they otherwise would include (context, motivation, why the question is interesting, what approaches they've tried and rejected). That doesn't always go over well.

Answer 3

I left a Comment for you on the Question before voting to close. It still seems worthwhile to improve the Question.

Let Readers know why the Question is worth posting

Was there something that makes this problem interesting or difficult? Merely being unable to find an exact duplicate of the Question does not mean it is a high-quality problem. Without any application this one seems to be a routine exercise in high-school level calculus, needing only polynomial differentiation, the quadratic formula, and a bit of attention to the signs of function values.

Let Readers know you intend to post a self-answer

Another Community member posted a detailed answer at about the same time you did, a few minutes later, unaware that you were posting one, and then self-deleted their Answer. This could have been avoided if you had announced your intention in the Question to post a self-answer.

Let Readers know the problem has been understood

Your setup of the problem is essentially a one-liner, although you then tack on that only cubics with three distinct real roots need to be considered. As a consequence the ratio of the (positive) relative maximum value to the (negative) relative minimum value will be a negative real number.

Pointing out this implication is one example of what might be done to let Readers see that you'd given the problem some thought. Too often problems are posted either in a jumbled form or in a verbatim "as assigned" form that frustrates Readers. It is unclear in those circumstances whether the difficulty the OP has is with the solution of the problem or with failing to understand what the problem is about.