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Math Help - check my work on quadratic equations?

  1. #1
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    check my work on quadratic equations?

    can someone check this for me?
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  2. #2
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    what about this one?
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  3. #3
    Super Member Bacterius's Avatar
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    No, both are wrong (first one in the answer, second one in the writing)

    \Rightarrow In the first one, you must write both answers :

    x = \frac{4}{\sqrt{5}} and x = - \frac{4}{\sqrt{5}}

    \Rightarrow The second one has the correct answer but is not correctly written. Here is an example of how it should be written :

    x^2 - 8x + 5 = 0

    x^2 - 8x = -5

    x^2 - 8x + 16 = 11

    (x - 4)^2 = 11

    x - 4 = \sqrt{11} or x - 4 = - \sqrt{11}

    x = \sqrt{11} + 4 or x = - \sqrt{11} + 4

    Thus x = 4 \pm \sqrt{11}



    EDIT : talking about the first question in this post ...
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  4. #4
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     \frac{-4\pm 2\sqrt{10}}{2}= -2\pm \sqrt{10}
    Last edited by pickslides; December 8th 2009 at 06:25 PM. Reason: Bad Latex
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  5. #5
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    You must show all your working

    What if I didn't know what the quadratic formula was?

    You're up to here:

     \frac {-4 \pm 2\sqrt10}{2}

    The next bit is wrong. You didn't factor 2 out of the -4.
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  6. #6
    Super Member Bacterius's Avatar
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    The other question you posted is wrong too
    I am not taking account of the quadratic equation written on it because I do not see the link with the following.

    Here is how you do it :

    \frac{-4 \pm \sqrt{40}}{2} = \frac{-4 \pm \sqrt{4 \times 10}}{2}

    = \frac{-4 \pm 2 \sqrt{10}}{2} = \frac{2(-2 \pm \sqrt{10})}{2} --> This is where you messed up : you did not factorize the -4.

    = -2 \pm \sqrt{10}

    Or, more conveniently :

    = 2 \mp \sqrt{10}
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  7. #7
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    can someone help me understand the factorization part?
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  8. #8
    Super Member Bacterius's Avatar
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    Remember that ab + ac = a(b + c). Here, you have :

    \frac{-4 \pm 2 \sqrt{10}}{2}

    This can be written :

    \frac{-2 \times 2 \pm 2 \sqrt{10}}{2}

    The common factor is two, so you factorize it over the addition. Since you are factorizing all the 2 (and not -2 !), they become 1 (some people prefer to remove them directly though) :

    \frac{2(-2 \times 1 \pm 1 \sqrt{10})}{2}

    Now you can cancel 2 out :

    -2 \times 1 \pm 1 \sqrt{10}

    Which is simplified to :

    -2 \pm \sqrt{10}

    Or, even more conveniently :

    2 \mp \sqrt{10}
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  9. #9
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    still dont really folllow, sry
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  10. #10
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    alright let's break it down.

    We have

    -4\pm2\sqrt10

    if we had 2x^2+4x

    we would factorise it by taking 2x out of the equation.

    So we divide all terms by 2x:

    x+2

    So same as -4\pm2\sqrt10

    we can take 2 out of the equation;

    So divide everything by 2
    you will get:  -2\pm\sqrt10

    I divided the -4 by 2 (which made -2) and 2 by 2 ( which made 1)

    Is this more clear now?
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  11. #11
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    i think i got it now, thx a bunch
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  12. #12
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    Cool!
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