document.write( "Question 1198491: find a polynomial function of lowest degree with rational coefficients and the following as some of its zeros. 0, -(square root)7, 1+i \n" ); document.write( "

Algebra.Com's Answer #832106 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Such function has the root of , which is conjugate to \r\n" );
document.write( "over the field of rational numbers, and the root 1-i, conjugate to 1+i \r\n" );
document.write( "over the field of real numbers.\r\n" );
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document.write( "So, the full list of the roots consists of 5 numbers {0, , , 1+i, 1-i}.\r\n" );
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document.write( "Thus your polynomial is\r\n" );
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document.write( "    p(x) =  = \r\n" );
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document.write( "         =  =  = .\r\n" );
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document.write( "You can transform it to any other equivalent form.\r\n" );
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