document.write( "Question 375885: Find a fourth degree polynomial function f(x) having only real coefficients,-1,4, and i as zeros, and f(2)=30 \n" ); document.write( "

Algebra.Com's Answer #267309 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
If $\"x=i\"$ is a solution, then so is $\"x=-i\"$ since complex solutions only come in complex conjuate pairs.
\n" ); document.write( " $\"f%28x%29=a%28x-1%29%28x-4%29%28x-i%29%28x%2Bi%29\"$
\n" ); document.write( " $\"f%28x%29=a%28x-1%29%28x-4%29%28x%5E2%2B1%29\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"f%282%29=a%282-1%29%282-4%29%282%5E2%2B1%29=30\"$
\n" ); document.write( " $\"a%281%29%28-2%29%285%29=30\"$
\n" ); document.write( " $\"a=-3\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"highlight%28f%28x%29=-3%28x-1%29%28x-4%29%28x%5E2%2B1%29%29\"$
\n" ); document.write( " \n" ); document.write( "

\n" );