The root of the function is such point [tex]x_0,[/tex] for which [tex]f(x_0)=0.[/tex]
The attached graph of the function [tex]f(x) = 2x^3 - 19x^2 + 57x - 54[/tex] shows, that the graph of the function intersects the x-axis in three points (2,0), (3,0) and (4.5,0).
This means that for
- x=2, f(2)=0;
- x=3, f(3)=0;
- x=4.5, f(4.5).
Thus, x=2, x=3 and x=4.5 are rational roots of the polynomial function f(x).
Answer: three rational roots.
