In chapter 7 of Spivak calculus, it is proved that if n is odd, then the 'n'th degree polynomial equation f(x) has a root. I do understand what goes into the proof and can follow steps easily.(adsbygoogle = window.adsbygoogle || []).push({});

But, my question is

1.How did they think of a proof like that?

2.By trial and error, did they find the set of values of x where the conditions for Intermediate Value theorem are satisfied?

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# I Spivak calculus, page 123 - if n is odd, then the 'n'th degree polynomial equation f(x) has a root

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