Question

The graph of f(x) = 2x3 – 19x2 + 57x – 54 is shown below. How many roots of f(x) are rational numbers

Answer 1

Answer:

3

Step-by-step explanation:

Answer 2

The root of the function is such point $x_0,$ for which $f(x_0)=0.$

The attached graph of the function  $f(x) = 2x^3 - 19x^2 + 57x - 54$ 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.