document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134217>Question 134217</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Just a little more help.<BR>\n" );
document.write( "Find the zeros of the polynomial function:<BR>\n" );
document.write( "F(x)=x³-6x²+9x\r<BR>\n" );
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document.write( "Thanks again </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98147 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=98147\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3-6x%5E2%2B9x ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3-6x%5E2%2B9x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E3-6x%5E2%2B9x ALIGN=MIDDLE  ALT=\"0=x%5E3-6x%5E2%2B9x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set f(x) equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%28x%5E2-6x%2B9%29 ALIGN=MIDDLE  ALT=\"0=x%28x%5E2-6x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out an \"x\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%28x-3%29%28x-3%29 ALIGN=MIDDLE  ALT=\"0=x%28x-3%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: if you need help with factoring, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)\r<BR>\n" );
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document.write( "Now set each factor equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=0 ALIGN=MIDDLE  ALT=\"x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=0 ALIGN=MIDDLE  ALT=\"x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Now solve for x in each case\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our solutions are \r<BR>\n" );
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document.write( "Notice if we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E3-6x%5E2%2B9x ALIGN=MIDDLE  ALT=\"y=x%5E3-6x%5E2%2B9x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  we can see that the roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > . So this visually verifies our answer.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+x%5E3-6x%5E2%2B9x%29+ ALIGN=MIDDLE  ALT=\"+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+x%5E3-6x%5E2%2B9x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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