document.write( "Question 1127284: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. -2, 2-i \n" ); document.write( "

Algebra.Com's Answer #743664 by ikleyn(52797) $\"\"$ $\"About$

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

\r\n" );
document.write( "\r\n" );
document.write( "For any polynomial with real coefficients, the roots go in pairs (complex number, conjugate complex number).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, at given condition, the roots of the polynomial are  -2, 2-i  and 2+i,\r\n" );
document.write( "\r\n" );
document.write( "and one possible polynomial is THIS\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    f(x) = (x+2)*(x-(2-i))*(x-(2+i)), which is the same as\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    f(x) = (x+2)*((x-2)+i)*((x-2)-i) = (x+2)*((x-2)^2+1).\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For your safety, ignore the post by @josgarithmetic, since it is W R O N G, as usual.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );