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?!
Best Answer
The difference is the following: whenever you have a function $f:X\to \mathbb R$ you say that $x^*$ is a zero of $f$ if $f(x^*) = 0$. On the other hand, the same $x^*$ is a root of the equation $f(x) = 0$. The rule of thumbs: zero refers to the function (e.g. polynomial) and root refers to the equation.