Answer:
Option 1.
Step-by-step explanation:
According to rational root theorem, all the potential rational roots of a function f(x) is defined as
[tex]roots=\dfrac{p}{q}[/tex]
where, p is a factor of constant term and q is the factor of leading coefficient.
The given function is
[tex]f(x)=9x^4-2x^2-3x+4[/tex]
Here, leading coefficient is 9 and factors of 9 are ±1, ±3, ±9.
Constant term is 4 and factors of 4 are ±1, ±2, ±4.
All the potential rational roots of f(x) are
[tex]\pm \dfrac{1}{9},\pm \dfrac{2}{9},\pm \dfrac{4}{9},\pm \dfrac{1}{3},\pm \dfrac{2}{3},\pm \dfrac{4}{3},\pm 1,\pm 2,\pm 4[/tex]
Therefore, option 1 is correct.
