The graph of f(x) = 2x^3 -19x^2 + 57x-54 is shown below. how many roots of f(x) are rational numbers? the options are 0,1,2,3

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