Chapter 9.3, Problem 55PPE

a.

To determine

To identify:

The spreadsheet formula you use to get value.

Answer to Problem 55PPE

The spreadsheet formula you use to get value is $6{\left(A_2\right)}^2-24$ .

Explanation of Solution

Given information:

Cell $=B2$

	$A$	$B$
$1$	$x$	$6x^{^}2-24=0$
$2$	$-3$
$3$	$-2$
$4$	$-1$
$5$	$0$
$6$	$1$
$7$	$2$
$8$	$3$

Now consider the following table:

$A$	$B$
$x$	$6x^{^}2-24=0$
$-3$	$6$
$-2$	$0$
$-1$	$-18$
$0$	$-24$
$1$	$-18$
$2$	$0$
$3$	$30$

from the table, it can be observed that the formula to get the values in cell $B2$ is as follows:

  $6{\left(A_2\right)}^2-24$

b.

To determine

To calculate:

The solution of given quadratic equation using the spreadsheet.

Answer to Problem 55PPE

The solution of given quadratic equation using the spreadsheet is $\pm 2$ .

Explanation of Solution

Given information:

Quadratic Question $=6x^{^}2-24=0$

	$A$	$B$
$1$	$x$	$6x^{^}2-24=0$
$2$	$-3$
$3$	$-2$
$4$	$-1$
$5$	$0$
$6$	$1$
$7$	$2$
$8$	$3$

Calculation:

Now consider the following table:

$A$	$B$
$x$	$6x^{^}2-24=0$
$-3$	$6$
$-2$	$0$
$-1$	$-18$
$0$	$-24$
$1$	$-18$
$2$	$0$
$3$	$30$

from the table, it can be observed that the value of $B$ equal to zero at $x=2,x=-2$ .

Therefore, the solution of $6x^{^}2-24=0$ are $\pm 2$

Because the solutions of the quadratic equation are the $x-$ values in column $A$ that makes the value in column $B$ equal to zero.

c.

To determine

To explain:

The use of the spreadsheet to approximate the solutions.

Answer to Problem 55PPE

Use the nearby values of $x$ in column $A$ to approximate the solution.

Explanation of Solution

Given information:

Quadratic Question $=6x^{^}2-24=0$

	$A$	$B$
$1$	$x$	$6x^{^}2-24=0$
$2$	$-3$
$3$	$-2$
$4$	$-1$
$5$	$0$
$6$	$1$
$7$	$2$
$8$	$3$

Now consider the following table:

$A$	$B$
$x$	$6x^{^}2-24=0$
$-3$	$6$
$-2$	$0$
$-1$	$-18$
$0$	$-24$
$1$	$-18$
$2$	$0$
$3$	$30$

To get the instance of a sign change in column $B$ . The solutions lies between the corresponding $x-$ values in column $A$ . Use the nearby values of $x$ in column $A$ to approximate the solution.