The correct response is that the URL you requested returns the "404" status to say there is nothing there.
You could set up a redirect to the root - but that would return a 301 HTTP status code, not a 404 status code.
In any case both methods are SEO suicide. Google may well flag them as "soft 404 errors" in WMT reports for your site.
You should return a custom error page for your 404 error, not the root index page. The custom page should explain that the requested content was not found, and that error page should then provide links to the root, your main section indexes, and to any special or featured content.
To do it any other way risks having your site flagged as being "technically broken".