document.write( "Question 869101: Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros.
\n" ); document.write( "4-i, square root 6 \n" ); document.write( "

Algebra.Com's Answer #524033 by Fombitz(32388) $\"\"$ $\"About$

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Complex roots always come in complex conjugate pairs.
\n" ); document.write( "Since $\"4-i\"$ is a root, then so is $\"4%2Bi\"$ }.
\n" ); document.write( "In order to have rational coefficients, you ned to have a difference of squares to eliminate the $\"sqrt%286%29\"$ .
\n" ); document.write( " $\"f%28x%29=%28x-sqrt%286%29%29%28x%2Bsqrt%286%29%29%28x-%284-i%29%29%28x-%284%2Bi%29%29\"$
\n" ); document.write( " $\"f%28x%29=%28x%5E2-6%29%28x%5E2-8x%2B17%29\"$
\n" ); document.write( " $\"f%28x%29=x%5E4-8x%5E3%2B11x%5E2%2B48x-102\"$ \r
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