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Math Help - Quadratic Equation via Formula

  1. #1
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    Quadratic Equation via Formula

    x^2+6x+13=0

    -6+-√6^2-4(1)(13)/2(1)

    -6+-√36-52
    -6+-√16/2
    -6+-√4/2
    -6-4/2=-5 or -6+4/2=-1
    Something seems a bit off though.
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  2. #2
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    Re: Quadratic Equation via Formula

    Quote Originally Posted by Past45 View Post
    x^2+6x+13=0

    -6+-√6^2-4(1)(13)/2(1)
    You forgot parentheses around -6+-√6^2-4(1)(13).

    Quote Originally Posted by Past45 View Post
    -6+-√36-52
    Should be (-6+-√36-52)/2

    Quote Originally Posted by Past45 View Post
    -6+-√16/2
    Again, parentheses around -6+-√16 are missing. Most importantly, 36 - 52 ≠ 16.
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  3. #3
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    Re: Quadratic Equation via Formula

    Quote Originally Posted by Past45 View Post
    x^2+6x+13=0

    -6+-√6^2-4(1)(13)/2(1)

    -6+-√36-52
    -6+-√16/2
    -6+-√4/2
    -6-4/2=-5 or -6+4/2=-1
    Something seems a bit off though.
    It is way off. The roots are complex numbers: \pm\sqrt{36-52}=\pm 4\bf{i}
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  4. #4
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    Re: Quadratic Equation via Formula

    Hu? Sorry a little confused. I did put the parentheses.. Only time in the book the parentheses are put in are when I plug in my numbers.

    The answer for this is suppose to -3-2i or -3+2i
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    Re: Quadratic Equation via Formula

    Quote Originally Posted by Plato View Post
    The roots are complex numbers: \pm\sqrt{36-52}=\pm 4\bf{i}
    You must mean the square roots of the discriminant, not the roots of the equation.

    Edit: added quote.
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  6. #6
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    Re: Quadratic Equation via Formula

    -6 √4i
    ----------- =
    2

    2(-3 √4i)
    ----------- =
    2

    the 2 cancels out so it will -3+-√2i

    so will it look like this?
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  7. #7
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    Re: Quadratic Equation via Formula

    Quote Originally Posted by Past45 View Post
    I did put the parentheses.. Only time in the book the parentheses are put in are when I plug in my numbers.
    The roots of the equation are \frac{-6\pm\sqrt{6^2-4\cdot1\cdot13}}{2\cdot 1}, which you wrote as -6+-√6^2-4(1)(13)/2(1). As you know, in the standard order of operations division comes before subtraction, so your formula is -6\pm\sqrt{6^2-\frac{4\cdot1\cdot13}{2\cdot1}. (In the text formula, it is also not clear where the square root ends.) And what about -6+-√16/2, which means -6\pm\sqrt{\frac{16}{2}} or -6\pm\frac{\sqrt{16}}{2}, but not \frac{-6\pm\sqrt{16}}{2}?

    In any case, the main mistake is that the discriminant is negative.
    Thanks from Past45
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  8. #8
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    Re: Quadratic Equation via Formula

    Nevermind I kind of see it, -6/2 =-3. Duh..
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    Re: Quadratic Equation via Formula

    thanks.

    Quote Originally Posted by emakarov View Post
    The roots of the equation are \frac{-6\pm\sqrt{6^2-4\cdot1\cdot13}}{2\cdot 1}, which you wrote as -6+-√6^2-4(1)(13)/2(1). As you know, in the standard order of operations division comes before subtraction, so your formula is -6\pm\sqrt{6^2-\frac{4\cdot1\cdot13}{2\cdot1}. (In the text formula, it is also not clear where the square root ends.) And what about -6+-√16/2, which means -6\pm\sqrt{\frac{16}{2}} or -6\pm\frac{\sqrt{16}}{2}, but not \frac{-6\pm\sqrt{16}}{2}?

    In any case, the main mistake is that the discriminant is negative.
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    Re: Quadratic Equation via Formula

    Quote Originally Posted by Past45 View Post
    -6 √4i
    √4i should be replaced by i√(16)
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    Re: Quadratic Equation via Formula

    Quote Originally Posted by emakarov View Post
    You must mean the square roots of the discriminant, not the roots of the equation.
    I did not say that those were the roots.
    I meant what I said.
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    Re: Quadratic Equation via Formula

    I am just going by how the book it showing me how to do it. But the square root of 16, is 4 though.

    Quote Originally Posted by emakarov View Post
    √4i should be replaced by i√(16)
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  13. #13
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    Re: Quadratic Equation via Formula

    Quote Originally Posted by Past45 View Post
    I am just going by how the book it showing me how to do it. But the square root of 16, is 4 though.
    Yes, and the equation roots are \frac{-6\pm4i}{2}=-3\pm2i.

    You should pay much more attention to arithmetic. Even though you are claiming that you are doing everything by the book, your posts in this thread contain numerous arithmetic errors.
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    Re: Quadratic Equation via Formula

    I just got it done, it is a lot simpler. The little errors are throwing me off. Thanks ne who.

    And yes, I go over the book and notes before anything. Thanks again.

    Quote Originally Posted by emakarov View Post
    Yes, and the equation roots are \frac{-6\pm4i}{2}=-3\pm2i.

    You should pay much more attention to arithmetic. Even though you are claiming that you are doing everything by the book, your posts in this thread contain numerous arithmetic errors.
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    Re: Quadratic Equation via Formula

    Quote Originally Posted by Past45 View Post
    x^2+6x+13=0
    -6+-√6^2-4(1)(13)/2(1)
    Properly bracketed (and you should show as equation):
    x = {-6 +- √[6^2 -4(1)(13)]} / [2(1)]
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