About one quarter of the roots of a 50 foot tall white pine were cut off at the drip line, all on the same side. Can I save this tree?
if they were cut at the dripline, and only on one side, I suppose that means a good bit less than 1/4 of the roots have been cut. Assuming that the tree is between 16 and 22" in diameter four and a half feet above ground, your structural root radius (that you can't safety be cutting within) will be 8-9'. This is the root plate, which supports the tree. Cutting into this will put you at risk of the tree coming down. That's your structural root zone. You also have to consider your critical root zone.
The critical root zone is the zone within which any cutting (or traffic from construction vehicles) will be extremely damaging to the tree. Do not work within this radius. Again assuming a tree diameter of 16 - 22", your critical rooting zone will be from 20 - 28', respectively.
If the roots on your tree were cut past that point, you should be fine. Mulching lightly (like 3") under the dripline will help recovery a lot. If the roots were cut inside the critical root zone, your tree may decline. Whether it will recover in that case depends partly on what the roots were cut for. If the soil was replaced (like if it was a trench for a line, and was backfilled), that's great. If the area the roots were cut is going to remain unviable for root growth (such as if you had a foundation put in, or regraded), things may be less bright.
In either case (of disturbing the critical root zone), there are a few steps you can take to help the tree survive. Maintain a layer of mulch under the tree (3-4" is good), keeping it off of the root flare, and have it out at least to the dripline, if possible. Also, reduce traffic (even foot traffic) as much as possible, to help prevent compaction.
I have very few details about your tree to go on, but I feel you will probably be fine, white pines can be quite resilient.