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Math Help - Where's the roots?

  1. #1
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    Where's the roots?

    Draw a single plot showing the parabola f(x)=x^2-4x+5 and where the roots are in relation to it.
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by shawsend View Post
    Draw a single plot showing the parabola f(x)=x^2-4x+5 and where the roots are in relation to it.
    There are no roots.
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by malaygoel View Post
    There are no roots.
    There are no real roots.
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  4. #4
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    Hello, shawsend!

    I don't know what they mean by "a single plot."
    Since the roots are complex, how are we to graph them?


    Draw a single plot showing the parabola f(x)=x^2-4x+5
    and where the roots are in relation to it.

    The roots are: . x \:=\:2 \pm i

    Where are they? . . . Well, they are not on the xy-plane

    If we had an i-axis coming out of the xy-plane,
    . . the graph might look like this:

    Code:
               y|
                |            *
                |
                *           *
                |*         *
                |  *     *
                |     *
                |     :
                + - - * - - - - x
               /     /
              /     *
             /   (2,0,1)
           i/

    One root is on the "floor" at (2,0,1).
    The other is (2,0,-1), one unit "behind" the xy-plane.

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  5. #5
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    Quote Originally Posted by Soroban View Post
    Hello, shawsend!

    I don't know what they mean by "a single plot."
    Since the roots are complex, how are we to graph them?



    The roots are: . x \:=\:2 \pm i

    Where are they? . . . Well, they are not on the xy-plane

    If we had an i-axis coming out of the xy-plane,
    . . the graph might look like this:

    Code:
               y|
                |            *
                |
                *           *
                |*         *
                |  *     *
                |     *
                |     :
                + - - * - - - - x
               /     /
              /     *
             /   (2,0,1)
           i/

    One root is on the "floor" at (2,0,1).
    The other is (2,0,-1), one unit "behind" the xy-plane.

    . . . nicer please, as in a nice illustration which clearly and unambiguously depicts the parabola, the (complex) zeros, and their relationship to one another as an educational tool to help students make the connection between the real-valued function and it's complex counterpart.
    Last edited by shawsend; July 6th 2009 at 06:06 AM.
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