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identify all real roots of x^3-9x^2+16x-8=0

  • math -

    let f(x) = x^3-9x^2+16x-8
    try x = ±1, ±2, ±4, ±8 , hoping to get f(x) = 0

    wow, after one try ...
    f(1) = 1 - 9 + 16 - 8 = 0
    so x-1 is a factor
    using synthetic division I had the other factor as
    x^2 - 8x + 8

    so x^2 - 8x + 8 = 0
    I will use completing the square , since the middle term is even

    x^2 - 8x + 16 = -8 + 16
    (x-4)^2 = 8
    x-4 = ±√8 = ± 2√2

    x = 4 ± 2√2 or x = 1

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