Some minority DULL shareholders objected strongly against a merging of the DULL and Exciting corporations, as they had been convinced that DULL's future was bright and would be worth far more once its current precarious financial situation was resolved. Now that the merger has been completed, despite their objections, what rights do these shareholders have

Shareholders will have rights according to the  shareholder agreement that they would have entered into, merger terms between the companies and applicable government laws and rules.

Explanation:

However it has to be ensured that the majority shareholder even after merger will have the fiduciary duty towards the minority shareholder and that they shall ensure that all benefits and rights are being given to the minority shareholder and all acts of the majority shareholder are in good faith.