document.write( "Question 1148822: I'm having trouble understanding how to solve this problem.
\n" ); document.write( "Question: Write a polynomial function with rational coefficients so that p(x)=0 has the given roots: sqrt(5), 2-i
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #770161 by ikleyn(52810) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Such a polynomial must have the root  ,  associated with ,  and the root  , associated with .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the polynomial, presented as the product of linear factors is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    p(x) = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The product of the first two factors is  .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The product of the last two factors is   = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the polynomial  p(x)  is  p(x) = ..\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You can multiply the last two quadratic polynomial to get the standard form, if you need.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In any case, the idea and the method are presented, so you can learn it from my post.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );