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Math Help - Square Root Problem

  1. #1
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    Square Root Problem

    We are nearing the end of my algebra class.. I understand almost everything. I am currently doing a review, but I am not sure what to do for this problem..

    Above the equation it says to use the discriminant to solve, but I dont believe this is a discriminant problem


    Im not sure how to write it out regularly, so I will try my best.

    Problem:

    The square root of... 9x^2 - 12x + 4


    Ive tried breaking down each # and variable seperatley but I dont understand how we are supposed to get to this answer:

    Absolute Value of 3x - 2


    Does anyone know what to do?
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  2. #2
    Super Member TheChaz's Avatar
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    Quote Originally Posted by gurrry View Post
    We are nearing the end of my algebra class.. I understand almost everything. I am currently doing a review, but I am not sure what to do for this problem..

    Above the equation it says to use the discriminant to solve, but I dont believe this is a discriminant problem


    Im not sure how to write it out regularly, so I will try my best.

    Problem:

    The square root of... 9x^2 - 12x + 4


    Ive tried breaking down each # and variable seperatley but I dont understand how we are supposed to get to this answer:

    Absolute Value of 3x - 2


    Does anyone know what to do?
    (I'll ignore the discriminant part...)

    Take (3x - 2).
    Square it.
    (3x - 2)^2 = 9x^2 - 12x + 4, which is exactly what you have under the radical.

    Now √(A^2) IS NOT (just) "A"!!!!!!!!!!!!!!!!

    It is the Absolute Value of A. Some even define the absolute value in this way.
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  3. #3
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    Quote Originally Posted by TheChaz View Post
    (I'll ignore the discriminant part...)

    Take (3x - 2).
    Square it.
    (3x - 2)^2 = 9x^2 - 12x + 4, which is exactly what you have under the radical.

    Now √(A^2) IS NOT (just) "A"!!!!!!!!!!!!!!!!

    It is the Absolute Value of A. Some even define the absolute value in this way.
    So basically I just needed to factor what was underneath the radical?
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  4. #4
    Super Member Quacky's Avatar
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    Edit: Just to reference the discriminant part again, have you worked out the discriminant?

    It's: 12^2-4(9)(4)=0

    What does that tell you about the quadratic?
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  5. #5
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    Quote Originally Posted by Quacky View Post
    Edit: Just to reference the discriminant part again, have you worked out the discriminant?

    It's: 12^2-4(9)(4)=0

    What does that tell you about the quadratic?
    It tells me that there is one rational solution because the discriminant becomes zero... but im not sure what that can do for me as far as how to get the answer...
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  6. #6
    Super Member TheChaz's Avatar
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    Quote Originally Posted by gurrry View Post
    It tells me that there is one rational solution because the discriminant becomes zero... but im not sure what that can do for me as far as how to get the answer...
    One solution means that the quadratic is a perfect square trinomial... (ax + b)^2
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