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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?
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.
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.