if the equation x^4 - x^3 + ax^2 + bx + 1 = 0 has four positive roots then find the value of a and b?

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  • Dave
    Lv 6
    7 years ago
    Favorite Answer

    four positive roots means 4 sign changes.

    so a>0 and b<0.

  • 7 years ago

    If the equation x^4 - x^3 + ax^2 + bx + 1 = 0 has four positive roots, it can be written as:

    (x - c)(x - d)(x - e)(x - f) = 0, where c,d,e,f are the roots.

    (x - c)(x - d)(x - e)(x - f) = x^4 - x^3 + ax^2 + bx + 1

    multiply it out and compare coefficients (i.e. you get c^2d+e on the left side with x^4 ==> c^2d+e = 1, etc.)

    From those equations you should be able to find a and b.

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