Chapter 4.4, Problem 1CFU

To determine

To identify: The possible rational roots for the equation $x^4-3x^2+6=0$ .

Answer to Problem 1CFU

  $\text{Possible rational roots: }\pm \text{1, }\pm \text{2, }\pm \text{3, }\pm \text{6}$

Explanation of Solution

Given information: $x^4-3x^2+6=0$

Calculation:

Given function

  $p\left(x\right)=x^4-3x^2+6=0$

According to the Rational Root Theorem in order to find all possible rational roots you must divide the factors of both p and q, where p = the constant term and q = the leading coefficient.

The function must be in standard form (highest degree to lowest degree).

Leading coefficient $\left(q\right)=1$

Constant term $\left(p\right)=6$

Factors of $q=\pm 1,$

Factors of $p=\pm 1,\pm 2,\pm 3,\pm 6$

After dividing each factors these are all the possible rational roots of the function.

Factors of $\frac{p}{q}=\frac{\pm 1,\pm 2,\pm 3,\pm 6}{\pm 1}$

  $=\pm 1,\pm 2,\pm 3,\pm 6$

  $\text{Possible rational roots: }\pm \text{1, }\pm \text{2, }\pm \text{3, }\pm \text{6}$