document.write( "Question 528299: \"Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value.
\n" ); document.write( "n=3; -3 and 6+2i are zeros; f(2)=100
\n" ); document.write( "f(x)= ?\r
\n" ); document.write( "\n" ); document.write( "Thank you! \n" ); document.write( "

Algebra.Com's Answer #349231 by scott8148(6628) $\"\"$ $\"About$

You can put this solution on YOUR website!
complex roots (zeros containing i's) occur in conjugate pairs; if 6+2i is a zero, then 6-2i is also\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "if \"r\" is a root (zero) of a function, then \"x-r\" is a factor\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "f(x) = a(x - 3)(x - 6 - 2i)(x - 6 + 2i) = a(x - 3)(x^2 - 12x + 40)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "use f(2)=100 to find the value of \"a\" \n" ); document.write( "

\n" );