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Math Help - solve

  1. #1
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    solve

    the zero of the polynomial 2x ^2009+3x^2008+2x^2007+3x^2006+.......+2x+3 is:
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  2. #2
    MHF Contributor
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    Quote Originally Posted by vungaralas View Post
    the zero of the polynomial 2x ^2009+3x^2008+2x^2007+3x^2006+.......+2x+3 is:
    Hint : 2x^{2009} + 3x^{2008} = x^{2008}(2x+3)

    You can factor out (2x+3)
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  3. #3
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    clarify pls

    can u give total solutions pls?
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  4. #4
    Senior Member Peritus's Avatar
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    Here's a slightly different approach:
    The polynomial can be written as follows:


    p(x) = \sum\limits_{m = 0}^{1004} {x^{2m} }  + \sum\limits_{n = 1}^{1005} {x^{2n - 1} }

    now from the rational root theorem we know that the rational roots of the polynomial must be from the following group of possible solutions:


     \pm 1, \pm \frac{1}<br />
{2}, \pm \frac{3}<br />
{2}, \pm 3

    the positive solutions are obviously impossible, so now using the formula for the sum of the geometric progression we can easily find that the correct solution is:

    <br />
 - \frac{3}<br />
{2}<br />
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  5. #5
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    thanx

    thank u pls reapond to my following queries
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