Rational Roots: What are the Other Names?

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SUMMARY

The discussion centers on the equivalence of "rational roots" and "rational zeroes" in polynomial equations, highlighting that both terms refer to the same mathematical concept. The distinction between roots and zeroes is clarified, noting that a root pertains to an equation while a zero pertains to a function. The conversation also addresses the variability of terminology across different mathematics courses, suggesting that students may encounter different names for the same concepts throughout their education, particularly in advanced topics such as differential equations.

PREREQUISITES
  • Understanding of polynomial equations and functions
  • Familiarity with the concepts of roots and zeroes in mathematics
  • Basic knowledge of algebraic terminology
  • Awareness of the Chinese Remainder Theorem and its applications
NEXT STEPS
  • Research the differences between roots and zeroes in polynomial functions
  • Explore the Chinese Remainder Theorem and its various interpretations
  • Study the implications of terminology differences in advanced mathematics courses
  • Review definitions and theorems in college algebra and differential equations
USEFUL FOR

Students of mathematics, educators teaching algebra and higher-level math, and anyone interested in the nuances of mathematical terminology and its implications in learning.

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I was finishing a test today when one of the questions towards the end asked to have all the rational roots listed of a polynomial. I looked at this question and I thought: "I have never heard of 'rational roots'". Though I have heard of rational zeroes, so I just assumed these two to be the same. So far, from my web search and comparison of my book they seem the same.
So I have a question to follow this (that I don't think is homework intensive, but): Are there any of other theorems which have other common names that I may encounter, does this happen often?
Maybe I did go spacecadet in class for a while and the professor might have mentioned that the two are the same/related, but...will this be a reocurring trend through an education in math, say, up to differential equations?
EDIT: this was in college algebra.
 
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Strictly speaking, an equation has a root, while a function, such as a polynomial, has a zero. A zero of a function, f(x), is a root of the equation f(x)= 0. It is, unfortunately, a distinction that is ignored by all but anal-rententive people like me!
 
To answer your question - some classes may have different terms for a single concept, and sometimes a syllabus will define something that you think you already know in a different way with a piossibly different meaning. Definitions rule for each class you take.

Explanations of the Chinese remainder theorem in the hands of different folks:

http://www-math.cudenver.edu/~wcherowi/courses/m5410/ctccrt.html

(This one has a proof and some "remarks" which are really limiting conditions or definitions)

http://planetmath.org/encyclopedia/ChineseRemainderTheorem.html

They don't look identical do they?
 
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