document.write( "Question 106201: The problem is as follows= Given that x=1+2i is a zero for the funtion g(x)=3x^3-2x^2+7x+20, determine the remaining zeros.\r
\n" ); document.write( "\n" ); document.write( "The only solutions I know are 1+2i and 1-2i but I am having trouble getting the rest. PlEASE HELP \n" ); document.write( "

Algebra.Com's Answer #77245 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!
The problem is as follows= Given that x=1+2i is a zero for the funtion g(x)=3x^3-2x^2+7x+20, determine the remaining zeros.
\n" ); document.write( "The only solutions I know are 1+2i and 1-2i but I am having trouble getting the rest. PlEASE HELP
\n" ); document.write( "

\r\n" );
document.write( "g(x) = 3x³ - 2x² + 7x + 20\r\n" );
document.write( "\r\n" );
document.write( "First divide synthetically by [x - (1+2i)]\r\n" );
document.write( "\r\n" );
document.write( "    1+2i | 3 -2      7     20\r\n" );
document.write( "         |    3+6i -11+8i -20\r\n" );
document.write( "           3  1+6i  -4+8i   0\r\n" );
document.write( "\r\n" );
document.write( "Now we have partially factored the polynomial g(x) this way:\r\n" );
document.write( "\r\n" );
document.write( "g(x) = [x - (1+2i)][3x² + (1+6i)x + (-4+8i)]\r\n" );
document.write( "\r\n" );
document.write( "Now we divide the second factor synthetically by [x - (1-2i)]\r\n" );
document.write( "\r\n" );
document.write( "    1-2i | 3  1+6i  -4+8i   \r\n" );
document.write( "         |    3-6i   4-8i\r\n" );
document.write( "           3  4      0\r\n" );
document.write( "\r\n" );
document.write( "Now we have completely factored the polynomial g(x) this way:\r\n" );
document.write( "\r\n" );
document.write( "g(x) = [x - (1+2i)][x - (1-2i)](3x + 4)\r\n" );
document.write( "\r\n" );
document.write( "Setting the first factor = 0 gives x = 1+2i, which you were given.\r\n" );
document.write( "Setting the second factor = 0 gives x = 1-2i, which you knew was\r\n" );
document.write( "a zero because it is the conjugate of 1+2i.\r\n" );
document.write( "Setting the third factor = 0,\r\n" );
document.write( "\r\n" );
document.write( "      3x + 4 = 0\r\n" );
document.write( "          3x = -4\r\n" );
document.write( "           x = \r\n" );
document.write( "\r\n" );
document.write( "That's the third zero. \r\n" );
document.write( "           \r\n" );
document.write( "Edwin

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

\n" );