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Math Help - How to factor the quadratic

  1. #1
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    How to factor the quadratic

    2^(2X) - 5 x 2^(X) + 6 = 0
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  2. #2
    Super Member angel.white's Avatar
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    Quote Originally Posted by stepho_145 View Post
    2^(2X) - 5 x 2^(X) + 6 = 0
    2^{2x} - 5*2^x + 6 = 0

    (2^x)^2 - 5*(2^x) + 6 = 0

    For simplicity, lets substitute 2^x with y

    y^2 - 5y + 6 = 0

    (y - 3)(y-2)= 0

    Now anti-substitute

    (2^x - 3)(2^x - 2)= 0
    Last edited by angel.white; April 8th 2008 at 08:47 PM.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by stepho_145 View Post
    2^(2X) - 5 x 2^(X) + 6 = 0
    Let y = 2^x.

    Then this equation becomes
    y^2 - 5y + 6 = 0

    Can you factor this?

    (By the way, I strongly discourage the use of "x" as a multiplication symbol at this point in your education. It looks too much like the variable x. You can use the * for multiplication if you need a symbol.)

    -Dan
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by stepho_145 View Post
    2^(2X) - 5 x 2^(X) + 6 = 0
    put y=2^x, then your quadratic becomes:


    y^2 - 5 y + 6 = 0

    which obviously factorises to:

    (y-2)(y-3)=0

    or reversing the substitution:

    (2^x-2)(2^x-3)=0

    RonL
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