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Math Help - Quadratic equation question (with absolute function)

  1. #1
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    Quadratic equation question (with absolute function)

    If "a" is strictly negative and is not equal to -2 thenthe equation

    x^2 + a |x| + 1 = 0

    a. cannot have any real roots
    b. must have exactly four real roots or zero real roots
    3. must have exactly 2 real roots
    4. must have 2 or 4 real roots

    please help me out on how to solve this question.

    thanks
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  2. #2
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    Quote Originally Posted by champrock View Post
    If "a" is strictly negative and is not equal to -2 thenthe equation

    x^2 + a |x| + 1 = 0

    a. cannot have any real roots
    b. must have exactly four real roots or zero real roots
    3. must have exactly 2 real roots
    4. must have 2 or 4 real roots

    please help me out on how to solve this question.

    thanks
    Hi

    If x > 0 the equation is x + a x + 1 = 0
    If x < 0 the equation is x - a x + 1 = 0

    In both cases if -2 < a < 0 there are no roots because the discriminant is < 0

    If a < -2 then the discriminant is > 0, you can show that there are 2 real roots which are both > 0 (in the case where x > 0) or both < 0 (in the case where x < 0). There are therefore 4 real roots.

    The answer is b
    Last edited by running-gag; April 1st 2009 at 11:09 AM.
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