Conifer Treet

[Azmin]

There is a conifer tree about a 3 feet away from the house which I moved into a couple of months ago. I was warned by a neighbour that the roots would, if they could not go downwards, work their way sideway and probably into the foundation. The tree was 15 feet high and I have now cut it down to about 8 feet high and have trimmed the sides. Will the roots still grow? Should I do anything else?