Question Tag using had better or would better

The following may be checked in for instance [this Wikipedia article].

In the UK, the usual question tag after a statement using an auxiliary mirrors the auxiliary in the statement but reverses polarity:

• He's tall, isn't he?

• She's not daft, is she?

• He can swim, can't he?

• He can't swim, can he?

• It's beautiful, isn't it!/?

• It's not good news, is it?

• She should apply for promotion, shouldn't she?

• She shouldn't hide her light under a bushel, should she?

• He would pass easily if he worked harder, wouldn't he?

• He wouldn't pass even if he worked harder though, would he./?

'Had better/rather' do have a more cohesive nature than say 'is really' ('would better' is not in any way unary, though 'would better be [used etc]' are used: 'she'd better' etc in these constructions is always a contraction of 'she had better' etc). See these Google 5grams:

But, though had better/rather' do have a cohesive nature, the form of the tag still reflects that required by the simplex verb:

• He'd better / He had better try harder, hadn't he!/?

References are not easy to find; this is a repeat of the answer given on UsingEnglish.com many years ago. Note that the expanded (but archaic-sounding) expanded version is 'He had better try harder, had he not!/?' (though doubtless in the days when this sounded natural the use of the exclamation mark for the exclamatory version would have been considered improper).

Note also that the non-reversed tag question, where it is the judgement of the speaker / reliability of received wisdom rather than the clinical accuracy of the statement that is being queried (of course some tag 'questions' are really just polite attention / focusing / coercing devices: 'You'd be stupid not to consider this / agree'), is sometimes used:

• He's only doing 6 hours homework a night. He'll never pass his A-Levels at this rate. He'd better try harder! ...

• He'd better try harder, had he?

.........

• He can swim, can he? So why is he shouting for help? In the shallow end!