document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=38937>Question 38937</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many zeros are there in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28X%29=X%5E3-4X%5E2%2B2X%2B1 ALIGN=MIDDLE  ALT=\"F%28X%29=X%5E3-4X%5E2%2B2X%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Can you please show the work so i too can understand.\r<BR>\n" );
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document.write( "Thank you  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #24385 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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/cgi-bin/show-face.mpl?user=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=24385\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well from<BR>\n" );
document.write( "f(x) = x^3 - 4x^2 + 2x + 1<BR>\n" );
document.write( "you can, by inspection, see that x = 1 is one of the zeroes, since f(1) = 0<BR>\n" );
document.write( "Now if you factor f(x) you get<BR>\n" );
document.write( "f(x) = (x - 1)(x^2 - 3x - 1)<BR>\n" );
document.write( "The second polynomial is not factorable but the zeroes can be found using the quadratic formula, so that<BR>\n" );
document.write( "x = 1 and<BR>\n" );
document.write( "x = (3 ± sqrt(13)) / 2<BR>\n" );
document.write( "Thus there are 3 zeroes,<BR>\n" );
document.write( "one rational and two irrational... </SPAN>\n" );
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