odd-equations-numberphile

# Interactive video lesson plan for: Odd Equations - Numberphile

#### Activity overview:

Second part to this video: http://youtu.be/shEk8sz1oOw
More links & stuff in full description below ↓↓↓

If the highest power of a function or polynomial is odd
(e.g.: x^3 or x^5 or x^4371) then it definitely has a solution (or root) among the real numbers. Here's a nice proof demonstrated by Prof David Eisenbud from the Mathematical Sciences Research Institute.

At 10:33 Prof Eisenbud intended to say "no rational roots" rather than "no real roots".

At 2:52 we should have put (2,5) rather than (2,4)

Also, Prof Eisenbud adds that "The Dedekind cut corresponding to the root is: (Rationals x where f(x) is less than or equal to zero) + (Rationals x where f(x) is greater than zero)"

Numberline stuff: http://youtu.be/JmyLeESQWGw

Dedekind cuts: http://en.wikipedia.org/wiki/Dedekind_cut

Support us on Patreon: http://www.patreon.com/numberphile

NUMBERPHILE
Website: http://www.numberphile.com/
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Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile

Numberphile T-Shirts: https://teespring.com/stores/numberphile
Other merchandise: https://store.dftba.com/collections/numberphile

Tagged under: numberphile,polynomial,equation,roots,solution

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