Chapter 2.3, Problem 8QR

To determine

To find:The solution of equation $x^3+2x-1=0$ with the help of graph.

Answer to Problem 8QR

The solution of equation $x^3+2x-1=0$ is $x=0.4533$ .

Explanation of Solution

Given information:The equation is $x^3+2x-1=0$ .

Calculation:

To graph a function $f\left(x\right)=x^3+2x-1$ , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press $\boxed{\text{Y}=}$ key and enter right hand side of the equation $f\left(x\right)=x^3+2x-1$ after the symbol ${\text{Y}}_1$ . Enter the keystrokes $\boxed{\text{X}}\boxed{^}\boxed{3}\boxed{+}\boxed{2}\boxed{\text{X}}\boxed{-}\boxed{1}$ .

The display will show the equation,

  ${\text{Y}}_{\text{1}}=\text{X}^3+2\text{X}-1$

Now, press the $\boxed{\text{GRAPH}}$ key and $\boxed{\text{TRACE}}$ key to produce the graph of given function in standard window as shown below.

  

Figure(1)

It can be observed from the graph, that the function $f\left(x\right)=x^3+2x-1$ meets the $x$ -axis at $x=0.4533$ .

Therefore, the solution of equation $x^3+2x-1=0$ is $x=0.4533$ .