Use the rational root theorem to list all possible rational roots for the equation 3x^3+9x-6=0

Asked by maham237 @ 27/12/2020 in Mathematics viewed by 329 People

Use the rational root theorem to list all possible rational roots for the equation.
3x^3+9x-6=0

Answered by maham237 @ 27/12/2020

Answer:

The possible rational roots are

$\pm 1, \pm 2,\pm3,\pm6,\pm \frac{1}{3},\pm \frac{2}{3}$

Step-by-step explanation:

We have been given the equation 3x^3+9x-6=0 and we have to list all possible rational roots by rational root theorem.

The factors of constant term are $1, 2, 3,6$

The factors of leading coefficient are $1,3,$

From ration root theorem, the possible roots are the ratio of the factors of the constant term and the factors of the leading coefficient. We include both positive as well as negative, hence we must include plus minus.

$\pm\frac{1,2,3,6}{1,3}\\\\ =\pm 1, \pm 2,\pm3,\pm6,\pm \frac{1}{3},\pm \frac{2}{3}$

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