Chapter 8.7, Problem 5OE

To determine

To find the possible rational roots of the equation.

Answer to Problem 5OE

The possible rational roots are $\pm 1,\pm 3,\pm 5\text{ and }\pm 15$

Explanation of Solution

Given information:

  $x^4-2x^2-16x-15=0$

Calculation:

The possible rational roots can be obtained as

  $x^4-2x^2-16x-15=0$

First find h and k

  $\begin{array}{l}h=1,3,5\text{ and 15 }\left[\begin{array}{l}h=\text{factor of the constant term of the polynomial}\\ \text{since, 15 is divisible by 1,3,5 and 15}\end{array}\right]\\ k=1\left[\text{k= factor of the cofficient of the highest-degree term}\right]\end{array}$

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

Therefore,

  $\pm \frac{1}{1}=\pm 1\text{ or }\pm \frac{3}{1}=\pm 3\text{ or }\pm \frac{5}{1}=\pm 5\text{ or }\pm \frac{15}{1}=\pm 15$

Hence,

The possible rational roots are $\pm 1,\pm 3,\pm 5\text{ and }\pm 15$