document.write( "Question 436866: Find all complex solutions of the equation: X^4-X^3+X^2-x=0. \n" ); document.write( "
Algebra.Com's Answer #302218 by stanbon(75887)\"\" \"About 
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Find all complex solutions of the equation:
\n" ); document.write( "X^4-X^3+X^2-x=0.
\n" ); document.write( "Factor:
\n" ); document.write( "x(x^3-x^2+x-1) = 0
\n" ); document.write( "---
\n" ); document.write( "So x= 0 is a Real root.
\n" ); document.write( "-------
\n" ); document.write( "Since the coefficients add to zero, x=1 is a Real root.
\n" ); document.write( "Use synthetic division:
\n" ); document.write( "1)....1....-1....1....-1
\n" ); document.write( ".......1.....0....1....|..0
\n" ); document.write( "----\r
\n" ); document.write( "\n" ); document.write( "Quotient: x^2+1
\n" ); document.write( "---
\n" ); document.write( "Factor:
\n" ); document.write( "(x-i)(x+i) = 0
\n" ); document.write( "x = i or x = -i
\n" ); document.write( "-------------------
\n" ); document.write( "Solutions: x= 0, or 1, or i, or -i.
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.\r
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