Chapter 2, Problem 27CR

a.

To determine

Find the real zeros of the givenequation algebraically.

Explanation of Solution

Given:

The given function is,

  $f\left(t\right)=t^3-3t$

Method:

Byusingfactorization method.

Calculation:

Consider,

  $f\left(t\right)=t^3-3t$

To find zeros of given function, put $f\left(t\right)=0$

  $\begin{array}{l}{t}^3-3t=0\\ \Rightarrow t\left(t^2-3\right)=0\\ \Rightarrow t\left(t-\sqrt{3}\right)\left(t+\sqrt{3}\right)=0\\ \Rightarrow t=0,\sqrt{3},-\sqrt{3}\end{array}$

So, the zeros of the given function are 0, $\sqrt{3}$ and $-\sqrt{3}$ .

b.

To determine

Draw the graph of given function using graphing utility.

Explanation of Solution

Given:

The given function is,

  $f\left(t\right)=t^3-3t$

Graph:

The graph of the above function is given below:

  

Interpretation:

Since, the graph of given function cuts the x-axis at $-1.732,0\text{and}1.732$ . Hence, the real zeros of the given function are $-1.732,0\text{and}1.732$ .

c.

To determine

To compare the results obtained algebraically and graphically.

Explanation of Solution

Given:

The given function is,

  $f\left(t\right)=t^3-3t$

Calculation:

By comparing the solution of the given function algebraically and graphically, We can say that the real zeros of the given function are x= $-1.732,0\text{and}1.732$ .