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Math Help - Writing equations in different forms

  1. #1
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    Writing equations in different forms

    I have a few questions I need help with:

    1. Can 2 different quadratic formulas have the same roots? Explain why or why not.

    2. Write the vertex form of (x-6)(x+2)

    3. Write x+x-6x in factor form

    4. For these questions the answer on the right are incorrect, I need the correct answer written in the original form of the answer on the right.

    x+5x-24=(x+3)(x-8)
    (x+2)(x-5)=x-10
    (x+3)=x+5

    Thanks for the help in advance!
    Last edited by Obiiscool; July 9th 2010 at 01:51 PM.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    For 1.

    Try with Vieta's formula...
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  3. #3
    Member Mathelogician's Avatar
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    Hi.

    1-No. if for ax+bx+c= 0 the roots are x1 and x2 and for dx+ex+f the roots are y1 and y2, we know that x1=y1 and x2=y2 (because we assumed that they have the same root) and by using the fact that: for a quadratic equation ax+bx+c= 0 which its roots are x1 and x2, we have x1 * x2=c/a and x1 + x2=-b/a, We see that at last, the components of the equations will be equal!
    3- x+x-6x =x(x+x-6)= x(x-2)(x+3)
    4-
    x+5x-24=(x-3)(x+8)
    (x+2)(x-5)=x-3x-10
    (x+2)(x-5) is the same last one!
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  4. #4
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    Thanks for those man. The last one was supposed to be this:

    (x+3)=x+5
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  5. #5
    Member Mathelogician's Avatar
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    So: (x+3)=x+6x+9
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  6. #6
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    Thanks. Anybody know how to write the vertex form of (x-6)(x+2)?
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  7. #7
    Member Mathelogician's Avatar
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    The vertex form of an equation is given by the formula: f(x) = a(x-h)^2 + k Where (h,k) is the vertex.
    So for yours: (x-6)(x+2) = x^2-4x+12 = (x-2)^2+8. Then the vertex form is: (2,8).
    See also: http://www.kutasoftware.com/FreeWork...0Parabolas.pdf
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