When you create an additional site collection under a managed path, the standard search settings do not show and advanced search link. Providing that your root site collection contains a search centre this can be fixed. I have created my root site collection based on the Publishing / Collaboration portal template.
I have created a site collection based on the team template. This is what the standard search drop down looks like.
Go to Site Actions, Site Settings. Then select Seach Settings from the Site Collection Administration group. Below is the default settings. Note how it defaults to do not custom scopes.
Now change the setting to use custom scopes, and enter the following relative URL /SearchCenter/Pages (as per the example on the page). See below.
Once you OK this a browse to the team site collection home you will now see the additional scopes on the drop down of ‘All sites’ and ‘People’ plus a link to advanced search.