Neighbor cut down a large tree on the property line without our knowledge the trunk of the 5foot or so diameter lies mostly on their side of the line but the roots and about 1 and a half feet are on our side .did they have a the right to remove this healthy tree without asking me?

For all practical purposes, cutting down the major vertical portion that was just on their land would kill what was on your land, so they were doing you a favor. They do have the right to take down what is on their land (and the tree obviously was within their border 100% when it was planted). Most laws allow people to even cut branches hanging over their land.

Should they have discussed it with you? It would have been the neighborly thing to do. But they didn't have to.
Some border disputes come under local ordinance, where towns set more detailed laws, so you can ask your town.
Border disputes often have so many variables that no law or ordinance can detail them all, and they end up in court.
Roots generally mean little except when they are tearing out a retaining wall or invading a foundation or waste pipes, and in most cases are the basis for a claim to get rid of them and the tree that is on a neighbor's property, not a claim to keep a tree.
Sorry.

If the tree was mostly on their property, then it was their tree. Clearly it was planted on their property and grew to where it encroached on your property.

So, yes they had every right to cut it down.