Approximate Solution of Equations

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Approximate Solution of Equations
Graphical Method
Example Solve the equation x2 2x - 1 0
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Method 1 Draw the graph y x2 2x - 1
y x2 2x - 1
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x -2.4
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Method 1 Draw the graph y x2 2x - 1
y x2 2x - 1
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x 0.4
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Method 2 Use of the given graph y x2

• Rewrite the equation as x2 -2x 1
• Add the line y -2x 1 on the same graph paper
• Note the x-coordinates of the points of
  intersection

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y x2
y -2x1
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Drawing Software
Winplot
http//math.exeter.edu/rparris
Graphmatica
http//www.pair.com/ksoft
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Approximate Solution of Equations
Method of Bisection
Example Solve the equation x3 - 3x2 5 0
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Step 1 Locate the root
y x3 - 3x2 5
The root lies between -2 and -1
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Step 2 Find the mid-point of the
interval that contains the root
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Step 3 Choose the half-interval that
contains the root
-1.5
-1.25
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-1.125
-1.0625
Root of x3 - 3x2 5 0 is
-1.1
(1 d.p.)
-1.0938
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Method of Bisection
Find the interval that contains the root
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-1.5
-5.13
-1.64
-1.25
Root of x3 - 3x2 5 0 is 1.1 (1d.p.)
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Method of Bisection
Use of Excel Spreadsheet