POTD Solving Quadratic Equations by pyb17727

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									                  POTD                             Solving Quadratic Equations
• Use the guess and check method to               • Objective:
  find the two solutions to this equation:        • To solve quadratic equations by using
                                                    square roots



          ( x ! 7 )2 = 25




                                                         Can you explain the
   The Square Root Method
                                                            difference?
• To solve an equation where the variable         • Describe in words how to solve these
  is being squared, we will take the                equations:
  square root.
  – Remember that when you take a square          x =9             x =9           x2 = 9
    root, you must always consider the positive
    and negative possibilities!
• Examples:
 x2 = 1     x2 = 4     x 2 = 144     x 2 = 900




                                                                                            1
            More Examples
• Other examples that you
                                                           Try These
  will see involve a more       ( x + 1) = 4
                                        2

  complicated variable                         • Solve:
  expression that is being
  squared.                                     ( x ! 3)2 = 9     ( 2x )2 = 64
• Here, we will need to be
  VERY careful when
  determining the solutions.
• You must consider the
  positive and negative
  possibilities.




            Other Examples                                 Try These
  • Other examples that you will see will      • Solve:
    resemble a linear equation.                                  x2
  • Here, you can start with linear            4x ! 1 = 99
                                                 2
                                                                    + 7 = 15
    techniques.                                                  2
  • Example:      2x 2 + 3 = 11




                                                                                2
        Can you explain the                                     Can you explain the
           difference?                                             difference?
• What do these equations have in                        • What do these equations have in
  common?                                                  common?

                                           x 2 +1 = 11                                 ( x ! 3)
                                                                                                  2
x +1 = 11            x +1 = 11                           x ! 3 = 25      x ! 3 = 25                   = 25




        Names for Solutions                                        Final Examples
• When solving quadratic equations, the
  solutions are called “REAL” solutions.                 • So right now, you cannot take the
                                                           square root of a negative number.
• This is because there are some
  situations where what seems                            • This means that expressions like the
  impossible actually has an application.                  ones below do not make sense.
  – Like with Alternating Current and Electricity!       • Example:
• Basically, you cannot find the square
  root of a negative number.                               !4         !9        !16          !25
  – But if you could….




                                                                                                             3
          Final Examples                     Solving Quadratic Equations
• And this means that the following         • Objective:
  equations do not make sense and           • To solve quadratic equations by using
  therefore have no solution:                 square roots
• Example:
                                            • Homework:
 x 2 = !49           2x 2 + 1 = !99           – Starts on page 567
                                              – See assignment sheet
We say that they have “no real solution.”




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