Would you say "He has homework to do, doesn't he?" or "He has homework to do, hasn't he?"? [duplicate]

I would normally say 'He has homework to do, doesn't he?' but I've heard some people say the other variant is correct.

Which one would you say is correct? Or are both of them correct?

Relevant link.

The English tag question is made up of an auxiliary verb and a pronoun. The auxiliary must agree with the tense, aspect and modality of the verb in the preceding sentence.

• If the verb is in the present perfect, for example, the tag question uses has or have;
• if the verb is in a present progressive form, the tag is formed with am, are, is;
• if the verb is in a tense which does not normally use an auxiliary, like the present simple, the auxiliary is taken from the emphatic do form;
• and if the sentence has a modal auxiliary, this is echoed in the tag

It seems to me that the easy way to remember these rules is to phrase the initial statement as a question, as it reveals the same auxiliary verb. In order of the above bullet points:

He has painted the house.
=> Has he painted the house?
=> He has painted the house, hasn't he?

He is painting the house.
=> Is he painting the house?
=> He is painting the house, isn't he?

He paints houses.
=> Does he paint houses?
=> He paints houses, doesn't he?

He will paint the house.
=> Will he paint the house?
=> He will paint the house, won't he?

Note that you can substitute all of these with past tense and the same structure will apply.

In your case, you are using present simply with no modal auxiliary, so the tag question is formed from the emphatic do:

He has homework to do, doesn't he?

Coincidentally, "doesn't" is completely unrelated to the earlier "to do". It has everything to do with the main verb being "to have" without any auxiliary. To prove this, we can change the example to not contain "to do":

He has houses to paint, doesn't he?

However, other links on the same topic reveal that these rules are very different from locale to locale (e.g. UK English uses "hasn't" much more frequently than US English), so these rules are not universally set in stone across the English speaking world.
I suspect UK English speakers would've used "hasn't he" in your example, or at least considered both options to be valid. But I'm no native UK English speaker so I'm not the best source on that.

It seems this is one of those cases where speakers of a certain English dialect will intuitively sense which verb is the right one to use, and it's hard to encapsulate all possible use cases in a simple rule that everyone agrees with.