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Math Help - Condition for real roots

  1. #1
    Senior Member pankaj's Avatar
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    Condition for real roots

    Find the values of a such that the equation

    x^4+ax^3+bx^2+ax+1=0

    has 3 different real roots.
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  2. #2
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    Quote Originally Posted by pankaj View Post

    Find the values of a such that the equation x^4+ax^3+bx^2+ax+1=0 has 3 different real roots.
    did you mean "exactly" or "at least" 3 distinct real roots? anyway, the main idea is to note that if x is a root, then \frac{1}{x} will be a root too.

    [for those who probably don't know, polynomials of this form can be easily reduced to a quadratic equation by putting x+\frac{1}{x}=t.]
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  3. #3
    Senior Member pankaj's Avatar
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    It means exactly 3 roots.Obviously one is a repeated root and the other two are different.Something like x_{1},x_{1},x_{2},x_{3}.

    x_{1},x_{2},x_{3} being all distinct
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