Second part to this video: http://youtu.be/shEk8sz1oOw

READ FULL DESCRIPTION FOR CLARIFICATIONS, EXTRA INFO, ETC.

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

Website: http://www.numberphile.com/

Numberphile on Facebook: http://www.facebook.com/numberphile

Numberphile tweets: https://twitter.com/numberphile

Google Plus: http://bit.ly/numberGplus

Tumblr: http://numberphile.tumblr.com

Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile

Videos by Brady Haran

A run-down of Brady's channels: http://bit.ly/bradychannels

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

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