Question

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 9x4 – 2x2 – 3x + 4?

Answer 1

The answer is the first choice - see picture for solution:

Answer 2

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

$roots=\dfrac{p}{q}$

where, p is a factor of constant term and q is the factor of leading coefficient.

The given function is

$f(x)=9x^4-2x^2-3x+4$

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

$\pm \dfrac{1}{9},\pm \dfrac{2}{9},\pm \dfrac{4}{9},\pm \dfrac{1}{3},\pm \dfrac{2}{3},\pm \dfrac{4}{3},\pm 1,\pm 2,\pm 4$

Therefore, option 1 is correct.