Question

List all the possible rational roots x^3 + x^2 -3x+12

Answer 1

Answer: See below

Explanation:

`$$Find the possible rational roots using the rational root theorem:$$x^(3)+x^(2)-3 x+12=0$$Select the coefficient of the leading term and the constant term:$1 x^(3)+x^(2)-3 x+12=0$\\Find the positive divisors of 12 and 1: \\\\Divisors of $12: 1,2,3,4,6,12$\\Divisors of $1: 1$\\Divide each of the divisors of 12 by 1 :\\$(1)/(1), (2)/(1), (3)/(1), (4)/(1), (6)/(1), (12)/(1)$2, \pm 3, \pm 4, \pm 6, \pm 12$$`

`$$Because both positive and negative values are valid candidates, the possible rational roots of $x^(3)+x^(2)-3 x+12=0$ are:$$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12`