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It is well-known. It is even known that you may take $R=(1+x)^m$ for large enough $m$. See, for example,

 https://prase.cz/kalva/short/soln/sh9711.html

  Note that by the real fundamental theorem of algebra, the general case reduces to the case $\deg P\leqslant 2$.

It is well-known. It is even known that you may take $R=(1+x)^m$ for large enough $m$. See, for example,  John Scholes's solution to Problem 11 of the 38th IMO 1997 shortlist. Note that by the real fundamental theorem of algebra, the general case reduces to the case $\deg P\leqslant 2$.

It is well-known. It is even known that you may take $R=(1+x)^m$ for large enough $m$. See, for example,

prase.cz/kalva/short/soln/sh9711.html

Note that by the real fundamental theorem of algebra, the general case reduces to the case $\deg P\leqslant 2$.

It is well-known. It is even known that you may take $R=(1+x)^m$ for large enough $m$. See, for example,

https://prase.cz/kalva/short/soln/sh9711.html

Note that by the real fundamental theorem of algebra, the general case reduces to the case $\deg P\leqslant 2$.

It is well-known. It is even known that you may take $R=(1+x)^m$ for large enough $m$. See, for example,

prase.cz/kalva/short/soln/sh9711.html

Note that be a real fundamental theorem of algebra, the general case reduces to the case $\deg P\leqslant 2$.

It is well-known. It is even known that you may take $R=(1+x)^m$ for large enough $m$. See, for example,

prase.cz/kalva/short/soln/sh9711.html

Note that by the real fundamental theorem of algebra, the general case reduces to the case $\deg P\leqslant 2$.