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Math Help - Quadratic Formula

  1. #1
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    Quadratic Formula

    1/2x^2+3/4x-1=0

    -3/4(+-)SQRT((3/4^2)-4(1/2)(-1) / 2(1/2)

    -3/4(+-)SQRT(9/16+2) / 1

    This is as far as I can get I do not see any errors yet the answer is supposed to be

    -3+-SQRT(41) /4

    I am clueless as to where the 41 comes from
    Last edited by Kromletch; January 18th 2011 at 11:27 AM.
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  2. #2
    A Plied Mathematician
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    The original problem:

    \dfrac{1}{2}\,x^{2}+\dfrac{3}{4}\,x-1=0.

    Quadratic formula gives

    x=\dfrac{-3/4\pm\sqrt{9/16-4(1/2)(-1)}}{1}=-3/4\pm\sqrt{9/16+2}=<br />
-3/4\pm\sqrt{(9+32)/16}=\dfrac{-3\pm\sqrt{41}}{4}.

    That's what I get. WolframAlpha gives the same.

    I conclude your book's answer is wrong.
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  3. #3
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    My apologies the books answer is yours as well i typed it incorrectly. How do you get (9 +32) / 16 out of 9/16+2
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  4. #4
    A Plied Mathematician
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    You have

    \dfrac{9}{16}+2=\dfrac{9}{16}+\dfrac{32}{16}=\dfra  c{9+32}{16}=\dfrac{41}{16}.

    This is the usual addition of fractions: get a common denominator and proceed.
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  5. #5
    Super Member Quacky's Avatar
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    Obviously it isn't necessary, but it would be easier to calculate if you multiplied the equation by four.

    2x^2 + 3x - 4 = 0 is so much easier to substitute into the formula, and it will probably save time as it's so much simpler to follow through.
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  6. #6
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    Quote Originally Posted by Kromletch View Post
    1/2x^2+3/4x-1=0
    This is as far as I can get I do not see any errors yet the answer is supposed to be
    -3+-SQRT(41) /4
    To start, that should be: [-3 +- SQRT(41)] /4 ; the extra brackets are IMPORTANT.

    GOOD IDEA to always get rid of fractions before doing anything else;
    so multiply your equation by 4: 2x^2 + 3x - 4 = 0 : get the picture?
    Now use the quadratic and you'll have no problems
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