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Math Help - Roots of polynomial function to 3rd power

  1. #1
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    Roots of polynomial function to 3rd power

    The three values of \cosh x given by the equation
    a\cosh 3x+b\cosh 2x=0
    where a and b are non-zero, are y_1, y_2, and y_3.
    Show that y_1y_2+y_2y_3+y_1y_3 is independent of a and b.

    a\cosh 3x+b\cosh 2x=0
    4a\cosh^3 x+2b\cosh^2 x-3a\cosh x-b=0
    I need to know the general formula for the roots? Or is there some simpler way?
    Thanks!
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  2. #2
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    In the cubic equation ax^3 + bx^2 + cx + d = 0, the sum of the product of roots αβ+βγ+γα = c/a.

    Hence in the given problem y1y2 + y2y3 + y3y1 = -3a/4a = -3/4.
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