recall from the "fundamental theorem of algebra", that the polynomial will have as many roots as its degree.
notice, this is a cubic polynomial, thus it has a 3rd degree, thus 3 roots as well.
now, a rational number is one you can write and represent as a "ration", or fraction.
by looking at the graph, check the picture below, the solutions, namely where the graph touches the x-axis, are
[tex]\bf 2\implies \cfrac{2}{1}\qquad \qquad 3\implies \cfrac{3}{1}\qquad \qquad 4.5\implies 4\frac{1}{2}\implies \cfrac{9}{2}[/tex]
