Question

According to the Rational Root Theorem, which statement about f(x) = 12x3 – 5x2 + 6x + 9 is true? Any rational root of f(x) is a multiple of 12 divided by a multiple of 9. Any rational root of f(x) is a multiple of 9 divided by a multiple of 12. Any rational root of f(x) is a factor of 12 divided by a factor of 9. Any rational root of f(x) is a factor of 9 divided by a factor of 12.

Answer 1

Answer:

Any rational root of f(x) is a factor of 9 divided by a factor of 12.

Step-by-step explanation:

Given:

f(x) = 12x³– 5x² + 6x + 9

Required; Rational root of f(x)

The rational root theorem states that: each rational solution

x = p⁄q, written in lowest terms so that p and q are relatively prime

Where

p = factors of the constant

q = factors of the lead coefficient.

Given that

f(x) = 12x³– 5x² + 6x + 9

The constant is 9

And the lead coefficient is 12

The factor of these two are

9; ±1 , ±3, ±9

12: ±1, ±2, ±3, ±4, ±6, ±12

Then the rational root of f(x) is

factor of 9 divided by a factor of 12.

Possible Rational Roots

= (±1 , ±3, ±9) / (±1, ±2, ±3, ±4, ±6, ±12)

The correct statement according to the rational root theorem is

The rational root of f(x) is

factor of 9 divided by a factor of 12

Answer 2

Any rational root of f(x) is a factor of 9 divided by a factor of 12.