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find a monic polynomial of lowest possible degree with rational coefficeients and having both 2 and 5-i roots.

 Oct 2, 2021
 #1
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I think this would be it.

 

\((x-2)*(x-5+i)*(x-5-i)\\ =(x-2)((x-5)^2+1)\\ =(x-2)(x^2-10x+26)\\ etc \)

 Oct 3, 2021

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