document.write( "Question 882934: Suppose that a polynomial function of degree 4 with rational coefficients has 6, 4, and sqrt2 as zeros. \r
\n" ); document.write( "\n" ); document.write( "Find the other zero \n" ); document.write( "

Algebra.Com's Answer #533183 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
The equation would have the form,
\n" ); document.write( " $\"f%28x%29=a%28x-6%29%28x-4%29%28x-sqrt%282%29%29%28x-b%29\"$
\n" ); document.write( "Since the coefficients are rational, then,
\n" ); document.write( "The product of the last two factors must cancel out the x term to eliminate the irrational coefficient.
\n" ); document.write( "That can be done by having a difference of squares since,
\n" ); document.write( " $\"%28x-c%29%28x%2Bc%29=x%5E2-c%5E2\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"highlight%28b=-sqrt%282%29%29\"$
\n" ); document.write( " $\"%28x-sqrt%282%29%29%28x%2Bsqrt%282%29%29=x%5E2-2\"$
\n" ); document.write( " \n" ); document.write( "

\n" );