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# Finding All Real Zeros of a Polynomial

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Author: Shirley Beil

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Tutorial

The following video will be available with closed captioning at:

http://youtu.be/Y_iZoBnfx2M

## P(x) = x^3 + 4x^2 + 3x − 2

The following video will be available with closed captioning at:

http://youtu.be/Wrkgpb4MImo

## P(x) = x^4 − 9x^3 + 9x^2 + 33x + 14

The 4 real zeros of this polynomial are: 7 -1, and (3 +/- √17)/2.
The +/- sign did not show up properly at the end of the video when I summarized results. THe narrative is correct.

The following video will be available with closed captioning at:

http://youtu.be/a_vxPiyEh9U

## P(x) = 4x^3 − 14x^2 + 25

The following video will be available with closed captioning at:

http://youtu.be/A2XXxjcj1hg

## Considering Descartes' Rule of Signs with P(x) = 2x^4 + 21x^3 + 64x^2 + 47x + 10

I didn't need to use the GC to look for positive irrational zeros because they would also then be real and we had already established that there were no positive real zeros!

The following video will be available with closed captioning at:

http://youtu.be/5GU642EA8iY

## Considering Descartes' Rule of Signs with P(x) = 4x^4 −25x^2 +6

The following video will be available with closed captioning at:

http://youtu.be/f9yJX0E_2Uo