The correct answer to this open question is the following.
The question is incomplete. Indeed, here we do not have a question, just a statement. After the statement, the full question must say:<em> "Decide if the situation jeopardizes the government's legitimacy."</em>
What is the situation? The statement above-mentioned.
So the situation is this:
Three top military generals overthrow the country's government. The generals are very popular with the citizens, who cheer by the thousands in streets across the country.
Under this situation, the legitimacy is not jeopardized because it was the people who supported the generals to overthrow the country's government. So we can say that the generals are legit because they received the support of the people and that is why they succeeded. The people believe in them.
Let's remember that in politics, the concept of legitimacy means that the people think that their ruler is the right one, the capable one, and has the support of the citizens.
The other three important concepts of a solid government are Power, Authority, and Sovereignty.