How could one sufficiently prove that a polynomial of odd degree in R[x] with no multiple roots must have an odd number of real roots?(adsbygoogle = window.adsbygoogle || []).push({});

My book just refers back to a Corollary that states every polynomial of odd degree in R[x] has a root in R. However it doesn't say, all roots are in R.

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# Proof about an odd degree polynomial

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