document.write( "Question 222446: A polynomial of lowest degree with rational coefficients which has 2, 3^1/2, 2i and 3i as zeroes would be of what degree? \n" ); document.write( "

Algebra.Com's Answer #166538 by jim_thompson5910(35256) $\"\"$ $\"About$

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Remember, all complex zeros come in conjugate pairs. So there's another zero -2i as well (since -2i is the complex conjugate of 2i).\r
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\n" ); document.write( "\n" ); document.write( "So there are 4 zeros: $\"2\"$ , $\"sqrt%283%29\"$ , $\"2i\"$ , and $\"-2i\"$ \r
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\n" ); document.write( "\n" ); document.write( "By the fundamental theorem of algebra, this means that there is a polynomial of degree 4 that has these 4 zeros. So this means that the smallest degree is 4. \n" ); document.write( "

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