Question

Identify the possible rational roots for the equation x^4-3x^2+6=0

Answer 1

`6, -6, 3, -3, 2, -2, 1, -1`

Explanation:

One is given the following equation, and the problem asks one to identify the rational roots of the equation:

`x^4-3x^2+6=0`

The rational root theorem states that the list of positive and negative factors of the constant term over the factors of the coefficients of the term to the highest degree will yield a list of the rational roots of the equation. Use this theorem to generate a list of all possible ration roots of the equation.

`(+-)(6,3,2,1)/(1)`

Now rewrite this list in a numerical format:

`6, -6, 3, -3, 2, -2, 1, -1`

This is the list of the possible rational roots. One has to synthetically divide each of these numbers by the given polynomial equation to find the actual rational roots. However, the problem only asks for the possible rational roots, not the actual rational roots, thus, this is not included.