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Math Help - Finding the roots of this equation: x^2 + (a - 1/a)x-1 = 0

  1. #1
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    Finding the roots of this equation: x^2 + (a - 1/a)x-1 = 0

    Any help would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by -DQ- View Post
    Any help would be greatly appreciated.

    The roots of this equation are


     x= \frac{-b\pm\sqrt{b^2-4ac}}{2a}

    where a = 1, b= a-1/a, c=-1
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  3. #3
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    Correct, but it is not a good idea to use "a" to represent two different quantities!

    Perhaps it would be better to write
    "The roots to the equation ix^2+ jx+ k= 0 are x= \frac{-j\pm\sqrt{j^2- 4ik}}{2i}. For this problem, i= 1, j= (a-1)/a, k= -1".

    (I am assuming that in the first post, "a- 1/a" meant "(a-1)/a", not "a- (1/a)".)
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  4. #4
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    This quadratic factorises as (x+a)(x-\tfrac1a). So the solutions of the equation are x=-a and x-\tfrac1a.

    (I am making the opposite assumption from HallsofIvy, namely that, "a- 1/a" meant "a- (1/a)", not "(a-1)/a".)
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