document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203583>Question 203583</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this problem, please help me:\r<BR>\n" );
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document.write( "i need to find the positive root, negative roots, and rational roots.\r<BR>\n" );
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document.write( "Given x^3-4x^2+2x+1=0\r<BR>\n" );
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document.write( "i got for the positive root=2<BR>\n" );
document.write( "negative root=1<BR>\n" );
document.write( "and im having trouble finding the rational roots.\r<BR>\n" );
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document.write( "thank you in advance!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153605 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=153605\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i need to find the positive root, negative roots, and rational roots. <BR>\n" );
document.write( "Given x^3-4x^2+2x+1=0 \r<BR>\n" );
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document.write( "Since the coefficients add up to zero, x=1 is a root<BR>\n" );
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document.write( "Using synthetic division you get the following:<BR>\n" );
document.write( "1)....1....-4....2....1<BR>\n" );
document.write( "........1.....-3...-1..|..0\r<BR>\n" );
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document.write( "Quotient: x^2 - 3x -1<BR>\n" );
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document.write( "Use the quadratic formula to get:<BR>\n" );
document.write( "x = [3 +- sqrt(9-4*1*-1)]/2<BR>\n" );
document.write( "x = [3 +- sqrt(13)]/2<BR>\n" );
document.write( "x = (3/2) + (1/2)sqrt(13) or x = (3/2)-(1/2)sqrt(13)<BR>\n" );
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document.write( "x = 1 is a rational root and is positive<BR>\n" );
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document.write( "x = (3/2)+(1/2)sqrt(13) is a positive root but not rational<BR>\n" );
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document.write( "x = (3/2)-(1/2)sqrt(13) is a negative root but not rational.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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