Question

List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros). (Enter your answers as a comma-separated list.)
S(x) = 6x^4 − x^2 + 3x + 12

Answer 1

Answer:

$\pm 1,\pm 2, \pm 3, \pm 4, \pm 6, \pm 12, \pm \dfrac{1}{2},\pm \dfrac{3}{2},\pm \dfrac{1}{3},\pm \dfrac{2}{3},\pm \dfrac{4}{3},\pm \dfrac{1}{6}.$

Step-by-step explanation:

According to the rational root theorem, the all possible rational roots of a polynomial are in the form of $\pm \dfrac{p}{q}$, where p is a factor of constant and q is a factor of leading coefficient.

The given polynomial is

$S(x)=6x^4-x^2+3x+12$

Here, leading term is 6 and constant is 12.

Factors of 6 are ±1, ±2, ±3 and ±6.

Factors of 12 are ±1, ±2, ±3, ±4, ±6 and ±12.

Using rational root theorem, the all possible rational roots of given polynomial is

$\pm 1,\pm 2, \pm 3, \pm 4, \pm 6, \pm 12, \pm \dfrac{1}{2},\pm \dfrac{3}{2},\pm \dfrac{1}{3},\pm \dfrac{2}{3},\pm \dfrac{4}{3},\pm \dfrac{1}{6}.$