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March 26, 2017

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What is the fundamental theorem of algebra of this polynomial in completed factored form? and how do I graph it?
f(x)=x^5-x^4+x^3-x^2+x-1

  • college algebra - ,

    it says there should be 5 roots.
    f(1) = 1-1+1-1+1-1 = 0
    so (x-1) is a factor
    by synthetic division I had
    (x-1)(x^4 + x^2 + 1)

    x^2 = (-1 ± √-3)/2 = (-1 ± i√3)/2

    now take √ of that again.
    So we get one real root of x=1 and 4 imaginary roots.

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