document.write( "Question 738468: What polynomial function with rational coefficients works for the given roots: 3i and √6 \n" ); document.write( "

Algebra.Com's Answer #450826 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
The imaginary roots always come in pairs, so
\n" ); document.write( "There are roots $\"+3i+\"$ , $\"+-3i+\"$ and $\"+sqrt%286%29+\"$
\n" ); document.write( " $\"+f%28x%29+=+%28+x+%2B+3i+%29%2A%28+x+-+3i+%29%2A+%28+x+-+sqrt%286%29%29+\"$
\n" ); document.write( " $\"+f%28x%29+=+%28+x%5E2+-+9%2A%28-1%29+%29%2A%28+x+-+sqrt%286%29+%29+\"$
\n" ); document.write( " $\"+f%28x%29+=+%28+x%5E2+%2B+9+%29%2A%28+x+-+sqrt%286%29+%29+\"$
\n" ); document.write( " $\"+f%28x%29+=+x%5E3+-+sqrt%286%29%2Ax%5E2+%2B+9x+-+9%2Asqrt%286%29+\"$
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