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Odd Equations

Odd Equations

Brady Haran
David Eisenbud, Algebra

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

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

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