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Topic: [ap-calculus] Rational Zero Theorem Test
Replies: 1   Last Post: Sep 16, 2012 8:19 PM

 Wilder Bob Posts: 406 Registered: 2/1/08
RE: [ap-calculus] Rational Zero Theorem Test
Posted: Sep 16, 2012 8:19 PM

I totally agree Richard -- I only mention it because a few years ago I was one of the instructors for a Precalc course at a local university and it was one of the arcane theorems presented and tested as part of that course .....

I assumed someone 'down the pike' thought it important .... but perhaps that assumption was overly generous.

In fact - since there were no precalculus courses when I was in high school, I'm not sure I ever saw it before I had to teach it!

Best - Bob

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Sent: Sunday, September 16, 2012 7:56 PM
To: Wilder Bob
Cc: AP Calculus
Subject: Re: [ap-calculus] Rational Zero Theorem Test

On Sep 16, 2012, at 6:06 PM, Wilder Bob wrote:

> Now - that said - a goal of many of our classes is also to prepare our students for success in whatever STEM courses follow in college, and some colleges may expect students to remember such details from a precalculus class,

I would hope that the Rational Zero Theorem is NOT one of those details. Suppose we create a polynomial of degree greater than 1 with integer coefficients but select those coefficients at random. The frequency of selecting coefficients of a polynomial with rational zeros is nearly ZERO. Then think about the fact that when polynomial functions are used as models for actual data, the coefficients are rarely integers. That is why the Rational Zero Theorem should be classified as one of the interesting antiques that used to occupy an inexcusably large portion of time in courses taught before calculus. Maybe that is why it disappeared from the AP Calculus course descriptions more than a decade ago.

Sincerely,

Richard Sisley

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