Chapter 8.8, Problem 8OE

To determine

To locate the real root of the equation between consecutive integers.

Answer to Problem 8OE

The root of the equation is in between $\text{0 and }1$ , $2\text{ and 3}$ .

Explanation of Solution

Given information:

The given equation is $x^4-2x^3-x+1=0$ .

Calculation :

First draw the graph of the equation.

  

According to graph the root lies between $\text{0 and }1$ , $2\text{ and 3}$

Check by substituting.

  $\begin{array}{l}P\left(0\right)=0^4-2\cdot 0^3-0+1=1>0\\ P\left(1\right)=1^4-2\cdot 1^3-1+1=-1<0\\ P\left(2\right)=2^4-2\cdot 2^3-2+1=-1<0\\ P\left(0\right)=3^4-2\cdot 3^3-3+1=25>0\end{array}$

The root of the equation is in between $\text{0 and }1$ , $2\text{ and 3}$ .