Chapter 6, Problem 18MCQ

To determine

Find the consecutive integer values of $x$ between which each real zero is located for the given function.

Answer to Problem 18MCQ

The consecutive integer values of $x$ between which each real zero are $x=-1$ to $x=0$ and $x=1$ to $x=2$ .

Explanation of Solution

Given:

The given function is $f\left(x\right)=3x^2-3x-1$ .

Calculation:

Draw a table for the values of $f\left(x\right)$ with respect to $x$ .

$x$	$f\left(x\right)=3x^2-3x-1$
$\begin{array}{l}-2\\ -1\\ 0\\ 1\\ 2\\ 3\end{array}$	$\begin{array}{l}17\\ 5\\ -1\\ -1\\ 5\\ 17\end{array}$

The graph of the function is given below.

  

There are two zeros because the changes in sign in between $x=-1$ to $x=0$ and $x=1$ to $x=2$ .

Hence the consecutive integer values of $x$ between which each real zero are $x=-1$ to $x=0$ and $x=1$ to $x=2$ .