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Math Help - Quadratic Enquiry

  1. #1
    Junior Member
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    Quadratic Enquiry

    Hi all, Many thanks to those who have offered valued help to my other posts.

    I think i'm starting to get the hang of this math lark

    Ok, down to the question, i have several questions that i have done my best to answer, I wondered if anyone would mind just looking over them for mistakes or wrong use of solutions please?

    (i) Solve by Factorization of quadratic formula:

    x(2) + 6x + 8 = 0

    By Factorization: (x + 4) (x + 2) = 0

    X = -4 X = -2

    By Quadratic Equation: -b +- sqrt b(2) - 4ac
    2a 2a

    - 6 +- sqrt 6(2) - (4x1x8)
    2x1 2x1

    = -3 +- 2
    2
    X = -4 X = -2.

    .................................................. ................................................

    (ii) 2x(2) + 11x + 14 = 0

    Using Quadratic Equation:

    - 11 +- sqrt 11(2) - (4 x 2 x 14)
    2x2 2x2

    = -2.75 +- 3
    4

    x = -3.5 x = -2

    .................................................. ................................................

    (iii) 6x(2) + 7x - 4 = 0

    Using Quadratic Equation ( to 3 d.p)

    - 7 +- sqrt 7(2) - (4 x 6 (-4)
    2x6 2x6

    -0.583 +- 12.041
    12

    x = 0.420 x = - 1.587

    .................................................. .................................................

    (iv) -7 + 11x - 3x(2) = 0

    Using Quadratic Equation ( to 3 d.p)

    *** do i transpose this so that x(2) is at the front***

    3x(2) - 11x + 7 = 0 ???? (x = 0.550 x =-4.220)

    Continueing with -7 + 11x - 3x(2) = 0

    - 11 +- sqrt 11(2) - (4 x (-7) x 3
    -14 -14

    x = -0.236 x = 1.810


    Phew, that the lot, I'm sorry to ask stupid questions, just that this is all new to me, and confidence is low
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  2. #2
    Super Member
    earboth's Avatar
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    Quote Originally Posted by Parton-Bill View Post
    Hi all, Many thanks to those who have offered valued help to my other posts.

    I think i'm starting to get the hang of this math lark

    Ok, down to the question, i have several questions that i have done my best to answer, I wondered if anyone would mind just looking over them for mistakes or wrong use of solutions please?

    (i) Solve by Factorization of quadratic formula:

    x(2) + 6x + 8 = 0

    By Factorization: (x + 4) (x + 2) = 0

    X = -4 X = -2 ........ OK

    By Quadratic Equation: -b +- sqrt b(2) - 4ac
    2a 2a

    - 6 +- sqrt 6(2) - (4x1x8)
    2x1 2x1

    = -3 +- 2
    2
    X = -4 X = -2. ........ OK

    .................................................. ................................................

    (ii) 2x(2) + 11x + 14 = 0

    Using Quadratic Equation:

    - 11 +- sqrt 11(2) - (4 x 2 x 14)
    2x2 2x2

    = -2.75 +- 3
    4

    x = -3.5 x = -2 ........ OK

    .................................................. ................................................

    (iii) 6x(2) + 7x - 4 = 0

    Using Quadratic Equation ( to 3 d.p)

    - 7 +- sqrt 7(2) - (4 x 6 (-4)
    2x6 2x6

    -0.583 +- 12.041
    12

    x = 0.420 x = - 1.587 ........ OK

    .................................................. .................................................

    (iv) -7 + 11x - 3x(2) = 0

    Using Quadratic Equation ( to 3 d.p)

    *** do i transpose this so that x(2) is at the front*** ........ Yes

    3x(2) - 11x + 7 = 0 ???? (x = 0.550 x =-4.220) ........ Where did you get these results from?

    ...
    3x^2 - 11x + 7 = 0~\implies~x=\dfrac{11}{2 \cdot 3} \pm\dfrac{\sqrt{ 121 - 4 \cdot 3 \cdot 7}}{2 \cdot 3}

    Therefore: x=\dfrac{11}{6} \pm\dfrac{\sqrt{ 37}}{6} ~\implies~x\approx 2.847~\vee~x\approx 0.820
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  3. #3
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    Joined
    Nov 2008
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    Danke :)

    Thanks very much for that, wasn't sure on the last one. will remember that.

    Thanks Again
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  4. #4
    Junior Member
    Joined
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    Quote Originally Posted by earboth View Post
    3x^2 - 11x + 7 = 0~\implies~x=\dfrac{11}{2 \cdot 3} \pm\dfrac{\sqrt{ 121 - 4 \cdot 3 \cdot 7}}{2 \cdot 3}

    Therefore: x=\dfrac{11}{6} \pm\dfrac{\sqrt{ 37}}{6} ~\implies~x\approx 2.847~\vee~x\approx 0.820
    The figures i calculated allowed for 7 to be -7, despite the tranposition, this would remain negative wouldn't it?
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