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Math Help - Complex numbers

  1. #1
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    Complex numbers

    New to this concept don't understand
    Find all the complex roots of the polynomial
    z
    z^6 -z^5+2z^4-5z^3+3z^2
    Compare the number of roots you obtain with the number predicted by the Fundamental
    Theorem of Algebra and discuss.
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  2. #2
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    Re: Complex numbers

    Well it's a sixth order polynomial. How many solutions do you expect from the fundamental theorem of algebra.

    Then you're trying to solve $\displaystyle \begin{align*} z^6 - z^5 + 2z^4 - 5z^3 + 3z^2 = 0 \end{align*}$, what methods do you know to solve polynomials? Can you at least pull out a factor?
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  3. #3
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    Re: Complex numbers

    It is fairly easy to find 4 (non-distinct) integer solutions.

    (The "rational root theorem" is useful here: If the polynomial equation a_nx^n+ a_{n-1}x^{n-1}+ \cdot\cdot\cdot+ a_1x+ a_0= 0 has rational root x= \frac{p}{q} then q must evenly divide the leading coefficient, a_n, and p must evenly divide the constant term, a_0. That gives you numbers to try.)
    Last edited by HallsofIvy; May 14th 2014 at 05:42 AM.
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