hi guys, i recently took over a website and redeveloped it and removed all old pages. however, i recently noticed that some links pointing to my site no longer exist, as in the page name! so the link is returning a 404 error

i would like to ideally redirect the user to the homepage of the site if they get the 404 error page, however i dont know what affect this will have on the search engines, if any, please advise.

also, if this is doable, what would be the quickest method of redirecting all dead links to my home page and would they count as normal links?

thanks guys