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Math Help - Zeros and Synthetic Division

  1. #1
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    Exclamation Zeros and Synthetic Division

    Solve:

    x^3+3x^2-5x-15=0


    (a)List all potential zeros




    (b)Do synthetic division to solve then finsh




    Thanks
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  2. #2
    Grand Panjandrum
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    Lets look at the very similar equation:

    x^3  + 2.x^2  - 7x - 14=0

    First thing to do is sketch the graph of:

    x^3  + 2.x^2  - 7x - 14

    to see if we can find the approximate location of its zeros.

    From the sketch in the attachment we see that this has zeros
    near -2.7, -2, and +2.7. Trying these out we find that -2 is
    an exact root of the cubic. So we may write:

    x^3  + 2.x^2  - 7x - 14\ =\ (x+2)(A.x^2+B.x+C)
    Now you can use synthetic division to find the quadratic, which
    in this case turns out to be:

    x^2-7
    which may be factorised either by inspection of by using the
    quadratic formula to find its roots, and hence its linear factors.

    So:
    x^3  + 2.x^2  - 7x - 14\ =\ (x+2)(x+\sqrt 7)(x-\sqrt 7)
    So the solutions of the cubic are -2,\ -\sqrt 7, +\sqrt 7.

    Your problem can be solved in a similar manner.

    RonL
    Attached Thumbnails Attached Thumbnails Zeros and Synthetic Division-cubic.png  
    Last edited by CaptainBlack; December 5th 2005 at 09:43 PM.
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