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Re: HSC 2013 4U Marathon $Call a polynomial $P(x)$ good if it satisfies the conditions in the question. So, if $P(x)$ is good, then $aP(x)+b$ where $a,c$ is rational will also be good. Moreover, if $P(a)=0$, then a must be rational. So, all of the roots of a good polynomial must also be...