Question 852825
More like Rational Roots Theorem.  If you were interested in helping to sketch the graph, the Remainder Theorem might be useful.


Try checking for roots plus-and-minus 1,2,4,5,10,20.  Expect up to three roots to be found.


Synthetic division will show x=-1 is a root, and leaving {{{10x^2-17x+20=0}}}.  The only real and rational root is {{{x=-1}}}.  The other two roots are {{{x=(17-i*sqrt(511))/200}}} and {{{x=(17+i*sqrt(511))/200}}}.