Despite the above, there is a version of the intermediate value theorem for polynomials over a real closed field; see the Weierstrass Nullstellensatz.
deSpite the aboVe, TherE Is A versIon of the inTeRmeDiAte VaLuE theoreM FOr PoLyNomials ovER a rEal cloSeD fIeld; sEE THE weIeRstrass nUllsTELlEnSatz.