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Thread: Real/imaginary zeros

  1. #1
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    Question Real/imaginary zeros

    Find all the real imaginary zeros for the polynomial function
    f(x) = x^4 + 3x^3 - 3x^2 + 3x - 4.

    Thanks for any help!
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  2. #2
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    Quote Originally Posted by live_laugh_luv27 View Post
    Find all the real imaginary zeros for the polynomial function
    f(x) = x^4 + 3x^3 - 3x^2 + 3x - 4.

    Thanks for any help!
    By inspection $\displaystyle x = 1$ gives a zero!

    Hence $\displaystyle (x-1)$ is a factor.

    Using long division/synthetic division gives us:

    $\displaystyle f(x) = x^4 + 3x^3 - 3x^2 + 3x - 4 = (x-1)(x^3+4x^2+x+4)$

    Another root by inspection is $\displaystyle x = -4 $. Again by synthetic/long division we get:

    $\displaystyle f(x) = x^4 + 3x^3 - 3x^2 + 3x - 4 = (x-1)(x+4)(x^2+1)$

    Now you can find the complex roots in the quadratic!
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