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The equation x cubed + 8x squared = 20 has two negative solutions between 0 and -8. Use trial and improvement to find these solutions. Give your answer to two decimal places.

Guest Feb 26, 2015

Best Answer 

 #1
avatar+26753 
+5

1.  Rewrite as x3 + 8x2 -20 = f(x) where we want the x that makes f(x) = 0.

Plot a graph:

graph

1. Guess x = -1,  f(-1) = -13

2. Guess x = -2  f(-2) = 4

 

3. Use f(-2)/(-2-x) = -f(-1)/(x- -1) to get the next value of x, namely x = -1.77 to 2 decimal places

When x = -1.77    f(-1.77) = -0.482  Not yet close enough to zero.  Because it is negative repeat step 3, but replace -1 and f(-1) with -1.77 and f(-1.77) respectively

 

4. Use f(-2)/(-2-x) = -f(-1.77)/(x- -1.77)  to get x = -1.80 to 2 decimal places

 

When x = -1.80  f(-1.80) = -0.09 

 

Repeat with

5. f(-2)/(-2-x) = -f(-1.80)/(x- -1.80) to get x = 1.80 to 2 decimal places

 

So one solution is x = 1.80 to 2 decimal places.

 

Try using the graph above to get two reasonable approximations to the other solution and repeat the above process.

.

Alan  Feb 26, 2015
 #1
avatar+26753 
+5
Best Answer

1.  Rewrite as x3 + 8x2 -20 = f(x) where we want the x that makes f(x) = 0.

Plot a graph:

graph

1. Guess x = -1,  f(-1) = -13

2. Guess x = -2  f(-2) = 4

 

3. Use f(-2)/(-2-x) = -f(-1)/(x- -1) to get the next value of x, namely x = -1.77 to 2 decimal places

When x = -1.77    f(-1.77) = -0.482  Not yet close enough to zero.  Because it is negative repeat step 3, but replace -1 and f(-1) with -1.77 and f(-1.77) respectively

 

4. Use f(-2)/(-2-x) = -f(-1.77)/(x- -1.77)  to get x = -1.80 to 2 decimal places

 

When x = -1.80  f(-1.80) = -0.09 

 

Repeat with

5. f(-2)/(-2-x) = -f(-1.80)/(x- -1.80) to get x = 1.80 to 2 decimal places

 

So one solution is x = 1.80 to 2 decimal places.

 

Try using the graph above to get two reasonable approximations to the other solution and repeat the above process.

.

Alan  Feb 26, 2015

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