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Find the complex zeros

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Find the complex zeros of the polynomial function. Write f in the factored form. f(x)=x^3-3x^2+7x-5
f(x)=

  • Find the complex zeros -

    a little synthetic division shows
    f(x) = (x-1)(x^2-2x+5)
    And it's easy from there

  • Find the complex zeros -

    First we have to find the real root, (every cubic has at least one real root)
    try x = 1 , y = 1 - 3 + 7 - 5 = 0 , so x-1 is a factor
    by synthetic division I got
    (x-1)(x^2 - 2x + 5) = 0
    So the real zero is when x=1

    for complex ...
    x^2 - 2x + 5= 0
    x^2 - 2x = -5
    x^2 - 2x + 1-5 + 1
    (x-1)^2 =-4
    x - 1 = ± 2i
    x = 1 ± 2i

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