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what are all of the possible rational roots for x to the third power- x squared-x +8=0?

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  1. x^3 - x^2 - x + 8 = 0

    tough one
    - it does not factor
    tried x = ±1, ±2, ±4 , none worked
    so no rational root

    what about real roots?

    let f(x) = x^3 - x^2 - x + 8
    for f(-1) = -1 -1 +1 +8 = 7
    for f(-2) = -8 - 4 + 2 + 8 = -2
    so there is a real root between -2 and -1
    nibbling away using my calculator, if found a root at
    appr x = -1.86
    f(-1.86) = -.034.. , close enough

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    posted by Reiny

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