document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=94191>Question 94191</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Given x^3 - 4x^2 + 2x + 1 =0<BR>\n" );
document.write( "(a)How many possible positive roots are there? <BR>\n" );
document.write( "(b)How many possible negative roots are there?<BR>\n" );
document.write( "(c)What are the possible rational roots?<BR>\n" );
document.write( "(d)Using synthetic substitution, which of the possible rational roots is <BR>\n" );
document.write( "   actually a root of the equation? <BR>\n" );
document.write( "(e)Find the irrational roots of the equation. (HINT: Use the quardratic      <BR>\n" );
document.write( "   formula to solve the depressed equation.)<BR>\n" );
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document.write( "(e)____________   \r<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 #68585 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=68585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given x^3 - 4x^2 + 2x + 1 =0<BR>\n" );
document.write( "(a)How many possible positive roots are there? <BR>\n" );
document.write( "(b)How many possible negative roots are there?<BR>\n" );
document.write( "(c)What are the possible rational roots?<BR>\n" );
document.write( "(d)Using synthetic substitution, which of the possible rational roots is <BR>\n" );
document.write( "   actually a root of the equation? <BR>\n" );
document.write( "(e)Find the irrational roots of the equation. (HINT: Use the quardratic      <BR>\n" );
document.write( "   formula to solve the depressed equation.)<BR>\n" );
document.write( "(a)_2 or 0 because f(x) has 2 changes of sign_<BR>\n" );
document.write( "(b)_1 because f(-x) has one change of sign_<BR>\n" );
document.write( "(c)_+1 or -1___________<BR>\n" );
document.write( "(d)_x = 1___________<BR>\n" );
document.write( "(e)_[3+sqrt13]/2 or [3-sqrt(13)]/2_   \r<BR>\n" );
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document.write( "Using synthetic division with x=1 you get:<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" );
document.write( "Using quadratic formula you get:<BR>\n" );
document.write( "x=[3+-sqrt(9-4*1*-1)]/2<BR>\n" );
document.write( "x=[3+-sqrt(13)]/2\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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