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how to find all the roots of the next two polinomials?: $x^{3}+6x^{2}-24x+160$ if one root is $2-2(3)^{1/2}i$ and $x^{5}-3x^{4}+4x^{3}-4x+4$ if $1+i$ is a double root

I don´t know how to solve this, I would really appreciate your help

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Hint

Notice that if a polynomial $P$ with real coefficients has a complex root $\alpha$ with multiplicity $m$ then its conjugate $\overline\alpha$ is also a root of $P$ with the same multiplicity and then $\left(x^2-2\operatorname{Re}(\alpha)x+|\alpha|^2\right)^m$ divides $P$.

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  • $\begingroup$ You're welcome. $\endgroup$ – user63181 May 28 '14 at 13:11
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Hint: Complex roots come in pairs. Whenever you have $a+bi$ as a root, you also have its complex conjugate $a-bi$ as a root, given a polynomial with real coefficients. This is called the complex conjugate root theorem.

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  • $\begingroup$ thank you!!! I´ll check the theorem $\endgroup$ – user153788 May 28 '14 at 13:10

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