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Creating Learning Networks for African Teachers

UNESCO PROJECT (Contract No. 408.302.9)

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SPREADSHEETS TUTORIAL

EXAMPLE : SOLVING POLYNOMINAL EQUATIONS


Example: Solve  2x3+ 6x2 - 9x -12 = 0

Solution:
To solve  2x3+ 6x2 - 9x -12 = 0, you have first to draw a graph of  y = 2x3+ 6x2 - 9x -12

PART 1 : Ploting the Graph of  y = 2x3+ 6x2 - 9x -12

Step 1: Plot a Graph of  y = 2x3 + 6x2 - 9x -12

 (a)    Type X in B7  and Y in C7

Block the range B8 through B24 and name this range x.

Insert ---> Name ----> Define

(b) In C8, type the formula  = 2*x^3 + 6*x^2 -9*x -12

(c) Type -5 in B8
     Autofill the cells B8 to B24 in steps of 0.5
    Block cells B8 to B24

 Edit ---> Fill ---> Series

Choose
Series in    : Columns
Type         : Linear
Step value : 0.5
Stop value : 3

Click OK
Copy the formula in C8 and paste it in the range C9 to C24.

(d)  Choose the the XY (Scatter) graph type shown below.
 

Complete the process of drawing the Chart (graph)
he graph is as shown below

Link to the Graph.

Part 2 : Solving 2x3 + 6x2 - 9x -12 = 0

We need to find the values of x when y = 0 or the intercepts on the X-axis. The graph of y = 2x2 + 6x2 - 9x -12 shows that there are three values of x: x1, x2and x3. Two of these values are negative and one positive.
To find the values x1, x2, x3 use the Goal Seek tool under Tools on the menu bar.

Goal  Seek adjusts the value in a specified cell until a formula that is dependent on that cell reaches a target value

In this case Goal Seek will adjust the value in cell B15 until until the formula in C15 reaches a target value of 0.

Note:

The values of Y change from:

-8 (negative) in cell C9   to  +7.25 (positive) in cell C10
 1 (positive) in cell C15  to   -6.25 (negative) in cell C16
-5.25 (negative) in cell C20 to +10 (positive) in cell C21

To obtain the values of x: x1, x2 and x3, use the Goal seek tool and set the values in cells C9 or C10, C15 or C16 and C20 or C21 to a target value of 0.


 

Use the following values
 
Set cell
  C9 C15  C20
To value
  0   0
0
By changing cell 
  B9  B15  B20


 
Link to the Graph

The polynomial  2x3 + 6x2 - 9x -12 = 0 has three solutions; x1 = -3.77, x2 = -0.93, x3 = 1.70
 
 

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