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Math Help - sing the quadratic formula with large numbers

  1. #1
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    using the quadratic formula with large numbers

    solving this using quadratic formula


    252x^2 + 188x - 225 = 0


    i got (-188 √188^2 - 4*252*-225)/504

    but even when I compute it I must be making a mistake because I do not get the right answer
    Last edited by kingsolomonsgrave; May 29th 2012 at 06:59 PM.
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    Re: sing the quadratic formula with large numbers

    i keep getting 379.5 and 519.753968 as the roots, which according to my text is wrong
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    Re: sing the quadratic formula with large numbers

    i found this online (from a quadratic calculator)


    −188512* square root 1
    ----------------------------
    504


    how does one know to multiply by the square root of one?

    I thought the formula called for the square root of b^2-4ac, and if b^2-4ac comes out to 262114 then it's root is 512, where does the 'times the square root of one' come in?

    MH
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    Re: using the quadratic formula with large numbers

    Quote Originally Posted by kingsolomonsgrave View Post
    252x^2 + 188x - 225 = 0
    x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}

    =\frac{-188\pm\sqrt{188^2-4(252)(-225)}}{2\cdot252}

    =\frac{-188\pm\sqrt{188^2+4\cdot252\cdot225}}{504}

    =\frac{-188\pm\sqrt{35\,344+226\,800}}{504}

    =\frac{-188\pm\sqrt{262\,144}}{504}

    =\frac{-188\pm512}{504}

    So

    x = \frac{-188+512}{504}=\frac{324}{504}=\frac9{14}

    or

    x = \frac{-188-512}{504}=-\frac{700}{504}=-\frac{25}{18}


    You can make the arithmetic a little bit easier by doing some factoring, but the above is what you should get through direct calculation.
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    Re: sing the quadratic formula with large numbers

    Quote Originally Posted by kingsolomonsgrave View Post
    i found this online (from a quadratic calculator)
    ...
    how does one know to multiply by the square root of one?
    512\cdot\sqrt1=512\cdot1=512. The format it gave you was probably a peculiarity of that specific calculator. I would guess that it gives all answers in a radical form.
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