What Are the Definitions of Zero and Root?

Date: 12/23/2003 at 18:32:46
From: Chapmann
Subject: Quadratics, specifically zeros and roots

What is a zero, and what is a root?  Different sources seem to be
giving me different answers, some of which contradict each other. 
What actually IS a root or zero?  When do I use root or zero?

Date: 12/23/2003 at 23:13:50
From: Doctor Peterson
Subject: Re: Quadratics, specifically zeros and roots

Hi, Chapmann.

The words are often misused, even by some textbooks that acknowledge 
they are going against tradition and catering to those who have become
accustomed to the wrong uses of the words.  The fact is, if the words
are used interchangeably you can still always figure out what is
meant, so there is no particular reason (other than logic) for making
a distinction.

But in my mind logic matters; the "correct" answer is that a function
has zeros where its value is zero, and an equation has roots (or
solutions) where it is true.  If we used the word "zero" for an
equation of the form f(x) = 0, it would be redundant, and would not
properly apply to solutions of equations of the form f(x) = g(x).  If
we used the word "root" for places where a function's value is zero,
there would be no reason for the term.  But when each is used in its
proper place, it makes complete sense.  (More or less!)

See this slightly fuller discussion:

  Origin of the Word Root
    http://mathforum.org/library/drmath/view/52673.html 

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 12/24/2003 at 14:41:32
From: Chapmann
Subject: Quadratics, specifically zeros and roots

Hi, thank you for the information.  It clears up a lot of unclear
points that I had before.