This may seem like a very basic question, but:
What exactly is the difference between a root of a polynomial, and a zero? Of course I realise that they are technically exactly the same thing, but there seem to be subtle rules as to when to use each term, and a couple of times in the past I have been told I am using "root" where I should be using "zero".
Is it generally accepted that one should use "root" in an algebraic context, and "zero" in a analytic context? If not, when should one use one or the other...and does it really matter?!