Is solving an equation the same as finding the roots?
Solution 1:
For the following pattern:
(roots of|zeros of|solutions to) (an equation|a function).
currently, the preferred usage is (in order):
- roots of an equation.
- zeros of a function.
- solutions to an equation.
- roots of a function.
"zeros of an equation" and "solutions to a function" are just plain wrong.
Presumably if one is talking about an equation, then 'roots' is preferred (or rather, it is just how people happen to speak).
This is all to say that these phrases are all interchangeable, but some are preferred to others in their contexts.