Chapter 8.8, Problem 10WE

To determine

To graph : the given polynomial P and approximate to the nearest half unit the real root(s) of the equation $P(x)=0$

Explanation of Solution

Given information :

The polynomial:

  $P(x)=x^4+x^3-10x^2-4x+10$

Graph :

As per the problem,

The polynomial:

  $P(x)=x^4+x^3-10x^2-4x+10$

Use graphing utility to graph the polynomial.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression, $P(x)=x^4+x^3-10x^2-4x+10$ , which is required to graph.

Step 4: Press GRAPH button to graph the functions.

  

Interpretation : The roots of the equation are the x -coordinates of the points where the graph intersects the x -axis. To the nearest half unit, the roots are $-3.5,-1,\text{ 1}$ and $2.5$ .