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. |
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