Advantages and Disadvantages of the 4 Methods of Solving Quadratic Equations

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Advantages and Disadvantages of the 4 Methods of
Solving Quadratic Equations
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Outline

• Factoring
• Square Root Property
• Completing the Square
• Quadratic Formula
• Advantages
• Disadvantages
• Summary

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Factoring

• x2  5x  6 0
• (x  2)(x  3) 0
• x 2 0 or x 3 0
• x -2 or x -3

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The Square Root Property

• 5x2 125
• x2 25 Divide both sides by 5 to isolate
  x2
• x v25 Apply the square root property
• x 5 Simplify

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Completing the Square

• x2 6x - 7 0
• x2 6x 7 Add 7 to both sides
• x2 6x 9 7 9 Add (b/2)2 to both sides
• (x 3)2 16 Factor the left side
• Use the Square Root Property to complete the
  solution
• x 3 4
• x -7, 1

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The Quadratic Formula

• For ax2 bx c 0, the value of x is given by
• Solve 3x2 2x 1 0

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Advantages
Method Advantages
Factoring Usually the fastest method
Square Root Property Simplest way to solve equations of the form (ax b)2 c
Completing the Square Can always be used
Quadratic Formula Can always be used
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Disadvantages
Method Disadvantages
Factoring Not all polynomials are factorable or they are difficult to factor
Square Root Property Few quadratic equations are given in the form (ax b)2 c
Completing the Square Requires more steps that take time and are more difficult than other methods
Quadratic Formula More difficult because of the square root but calculators can simplify its use
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Summary

1. Try factoring first because it is easier.
2. Completing the Square and the Quadratic Formula
   can always be used but they are a bit more
   difficult.
3. If the equation is in the form (ax b)2 c, use
   the square root property.

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Questions?