Solving Quadratic Equations

1
Solving Quadratic Equations

• by the Square Root Method

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Square Root Method

• Use if there is no linear term. (i.e. B 0)
• Get the Quadratic Term on one side and the
  Constant on the other side.
• Simply take the Square Root of Both Sides.

3
Square Root Method
Be sure to give both the positive and negative
answers!
4
Square Root Method
Be sure to give both the positive and negative
answers!
5
Solving Quadratic Equations

• by Completing the Square

Goal Turn the problem into a Square Root
Problem
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Completing the Square

• Take HALF the coefficient of the linear term
  (i.e. B ) and square.
• Example x2 8x c
• Example x2 12x c
• Example x2 9x c

c 16
c 36
c 81/4
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Lesson 4 Contents
Example 1 Equation with Rational Roots Example
2 Equation with Irrational Roots Example
3 Complete the Square Example 4 Solve an Equation
by Completing the Square Example 5 Equation with
a ? 1 Example 6 Equation with Complex Solutions
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Example 4-1a
Answer The solution set is 15, 1.
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Example 4-1b
Answer 3, 13
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Example 4-2a
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Example 4-2a
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Example 4-2a
Check Use the ZERO function of a graphing
calculator. The approximate zeros of the related
function are 1.5 and 8.5.
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Example 4-2b
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Example 4-3a
15
Example 4-3b
Answer 9 (x 3)2
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Example 4-4a
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Example 4-4a
Answer The solution set is 6, 2.
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Example 4-4b
Answer 6, 1
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Example 4-5a
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Example 4-5a
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Example 4-5a
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Example 4-5b
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Example 4-6a
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Example 4-6a
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Example 4-6a
Check A graph of the related function shows that
the equation has no real solutions since the
graph has no x-intercepts. Imaginary solutions
must be checked algebraically by substituting
them in the original equation.
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Example 4-6b