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Using high school algebra for a natural approach to derivatives and continuity

Published online by Cambridge University Press:  17 October 2018

R. Michael Range
R. Michael Range*
Affiliation:
Department of Mathematics, State University of New York at Albany, Albany, NY 12222USA e-mail: range@math.albany.edu
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Extract

The quadratic equation is a central topic in high school algebra. It provides the simplest generalisation of the familiar linear equation, and finding its roots introduces students to a non-trivial problem that requires the application of new techniques, such as completing the square and/or factorisation into linear factors involving the roots. It also introduces the student to the phenomenon of repeated roots, which opens the door to a discussion of multiplicities of roots. Furthermore, it naturally exposes the student to the case where the equation has no real roots, a phenomenon that could also be used to introduce the student to complex numbers.

Type
Articles
Information
The Mathematical Gazette , Volume 102 , Issue 555 , November 2018 , pp. 435 - 446
Copyright
Copyright © Mathematical Association 2018 

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References

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