Chapter 8.7, Problem 3OE

To determine

To find the possible rational roots of the equation.

Answer to Problem 3OE

The possible rational roots are $\pm 1,\pm 2,\pm 4\text{ and }\pm \text{8}$

Explanation of Solution

Given information:

  $x^3-3x^2+2x-8=0$

Calculation:

The possible rational roots can be obtained as

  $x^3-3x^2+2x-8=0$

First find h and k

  $\begin{array}{l}h=1,2,\text{4 and 8 }\left[\begin{array}{l}h=\text{factor of the constant term of the polynomial}\\ \text{since, 8 is divisible by 1,2,4 and 8}\end{array}\right]\\ k=1\left[\text{k= factor of the cofficient of the highest-degree term}\right]\end{array}$

  $$ All possible rational roots are in the form of $\pm \frac{h}{k}$

Therefore,

  $\pm \frac{1}{1}=\pm 1\text{ or }\pm \frac{2}{1}=\pm 2\text{ or }\pm \frac{4}{1}=\pm 4\text{ or }\pm \frac{8}{1}=\pm 8$

Hence,

The possible rational roots are $\pm 1,\pm 2,\pm 4\text{ and }\pm \text{8}$