the graph of f(x) = 4x3 – 13x2 + 9x + 2 is shown below.
how many roots of f(x) are rational numbers?
a.) 0
b.) 1
c.) 2
d.) 3

One rational root.

B is correct.

Step-by-step explanation:

Given: The graph of

First we factor the given function.

Factor of f(x)

f(2)=0 , x-2 must be factor of f(x)

Because f(2)=0

So, x=2 is rational root of f(x)

Now we find another root using quadratic formula.

where, a=4, b=-5 and c=-1

Another roots are,

So, these are irrational root because is irrational.

Hence, The given function has 1 rational root and 2 irrational roots.