document.write( "Question 141517: Find a polynomial function of lowest degree with rationl coefficients that has the given numbers as some of its zeros.
\n" ); document.write( "-8i, square root 8 \n" ); document.write( "

Algebra.Com's Answer #103134 by solver91311(24713) $\"\"$ $\"About$

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Both complex and irrational roots come in conjugate pairs. That is, if you have a root of the form $\"a%2Bbi\"$ , there must also be a root $\"a-bi\"$ . Likewise, if $\"a%2Bsqrt%28b%29\"$ is a root, then $\"a-sqrt%28b%29\"$ is also a root.\r
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\n" ); document.write( "\n" ); document.write( "Your roots are in these forms because $\"-8i=0-8i\"$ and $\"sqrt%288%29=0%2Bsqrt%288%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "A number $\"alpha\"$ is a zero of a polynomial function if and only if $\"x-alpha\"$ is a factor of the polynomial, so:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-8i%29%28x%2B8i%29%28x-sqrt%288%29%29%28x%2Bsqrt%288%29%29\"$ are the factors of your minimum (4th) degree polynomial. So get busy multiplying. \n" ); document.write( "

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