document.write( "Question 1102277: One root of $\"x%5E4+-+3x%5E2+-+4+=+0\"$ is 'i'. What are the other three roots? \n" ); document.write( "

Algebra.Com's Answer #716940 by josgarithmetic(39617) $\"\"$ $\"About$

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document.write( "Possible rational roots to try:  -4, -2, -1, 1, 2, 4\r\n" );
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document.write( "-1   |    1   0    -3   0    -4\r\n" );
document.write( "     |        -1    1   2    -2\r\n" );
document.write( "     ---------------------------------\r\n" );
document.write( "         1   -1    -2   2     -6\r\n" );
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document.write( "-2   |    1   0    -3   0    -4\r\n" );
document.write( "     |       -2     4   -2    4\r\n" );
document.write( "     ---------------------------------\r\n" );
document.write( "         1   -2    1    -2   0        -2 is a root, (x+2)\r\n" );
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document.write( "2     |    1   -2    1    -2\r\n" );
document.write( "      |         2    0     2\r\n" );
document.write( "      ----------------------------\r\n" );
document.write( "           1    0    1     0          2 is a root, (x-2)\r\n" );
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\n" ); document.write( "\n" ); document.write( "Other roots are found using $\"x%5E2%2B1=0\"$ , from the result of the last synthetic division shown.\r
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\n" ); document.write( "\n" ); document.write( "Note the use of 'i' in i^2=-1, imaginary number i.
\n" ); document.write( " $\"i=-sqrt%28-1%29\"$ or $\"i=sqrt%28-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B1=0\"$
\n" ); document.write( " $\"x%5E2=-1\"$
\n" ); document.write( " $\"system%28x=-sqrt%28-1%29%2Cor%2Cx=sqrt%281%29%29\"$
\n" ); document.write( " $\"system%28x=-i%2Cor%2Cx=i%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "--------------------------------
\n" ); document.write( "ALL THE ROOTS:
\n" ); document.write( " $\"system%28-2%2C2%2C-i%2Ci%29\"$
\n" ); document.write( "------------------------------- \n" ); document.write( "

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