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Math Help - [SOLVED] How to solve this question?

  1. #1
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    [SOLVED] How to solve this question?

    Given that the roots of the equation  x^2 + ax + (a + 2) = 0 differ by 2, find the possible values of the constant a. Hence, find the possible values of the roots of the equation.

    This is my solution:
    2\alpha + 2 = -a____(1)
    \alpha(\alpha + 2) = a + 2____(2)

    From (1),
    \alpha = \frac{-a - 2}{2}____(3)

    Sub (3) into (2),

    (\frac{-a - 2}{2})(\frac{-a - 2}{2} + 2) = a + 2
    (-a - 2)^2 + 2(-a - 2) - 8 = 0
    a^2 + 4a + 4 - 2a - 4 -8 = 0
    a^2 + 2a - 8 = 0
    (a + 4)(a - 2) = 0

    Hence, I got the answer a = -4 or a = 2 but in the book the answers are a = 6 or a = -2. Where have I gone wrong?
    Last edited by mark1950; June 30th 2009 at 02:02 AM.
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  2. #2
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    Hey...I've just found out the problem and solved it. Sorry if this question troubled your inks.
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