When you click in the search field at the top of every page, you get shown some extra information for searching. It includes a brief explanation about the search syntax as well as link to show more. However, it also includes a button that leads you to ask a question.
When searching I expect to avoid asking a question by finding the answer first. Even if I do decide to make a question, there is a different button on top of the page that will leads to the question interface.
So, a lot of times searching and asking are not related. When they are (because you're looking for prior relevant questions but can't find any), I do not think the "Ask a question" is not needed in the search form. Including screenshots to illustrate this:
Removing the button seems like it would alleviate the problem but it might be even better to change it to an actual search button which is also missing: