Question

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

Answer 1

Answer: See below

Step-by-step explanation:

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

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