document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134721>Question 134721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Fundamental Theorem of Algebra<BR>\n" );
document.write( "Use the given zero to find the remaining zeros of each polynomial function.\r<BR>\n" );
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document.write( "P(x)=x^4-6x^3+71x^2-146x+530;  2+7i<BR>\n" );
document.write( "x intercepts = 2+7i & 2-7i<BR>\n" );
document.write( "x=2-7i<BR>\n" );
document.write( "=x-2+7i=0=(x-(2-7i))=0<BR>\n" );
document.write( "(x-(2-7i))(x-(2+7i))=<BR>\n" );
document.write( "x^2-x(2+7i)-x(2-7i)+(2+7i)(2-7i)=<BR>\n" );
document.write( "x^2-2x-7xi-2x+7xi+53=<BR>\n" );
document.write( "x^2-4x+53=<BR>\n" );
document.write( "x^4-6x^3+71x^2-146x+530/x^2-4x+53=<BR>\n" );
document.write( "x^2-2x+10=<BR>\n" );
document.write( "(x^2-4x+53)(x^2-2x+10)<BR>\n" );
document.write( "Now I'm stuck.  Could really use some help<BR>\n" );
document.write( "Thanks so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98553 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=98553\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Everything you have done so far is absolutely correct, but you stopped short of saying that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-6x%5E3%2B71x%5E2-146x%2B530=%28x%5E2-4x%2B53%29%28x%5E2-2x%2B10%29=0 ALIGN=MIDDLE  ALT=\"x%5E4-6x%5E3%2B71x%5E2-146x%2B530=%28x%5E2-4x%2B53%29%28x%5E2-2x%2B10%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > =>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B53=0 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B53=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2B10=0 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You already have the roots for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B53=0 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B53=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > since you were given one of them and used it and its conjugate to derive the trinomial in the first place.  Now all you need is the roots of the quotient polynomial that came from division of the quartic by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B53 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B53\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  In other words, just solve\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2B10=0 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This one adapts readily to completing the square:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x=-10 ALIGN=MIDDLE  ALT=\"x%5E2-2x=-10\"   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%5E2-2x%2B1=-10%2B1 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B1=-10%2B1\"   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=%28x-1%29%5E2=-9 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2=-9\"   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-1=3i ALIGN=MIDDLE  ALT=\"x-1=3i\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=-3i ALIGN=MIDDLE  ALT=\"x-1=-3i\"   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=1%2B3i ALIGN=MIDDLE  ALT=\"x=1%2B3i\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1-3i ALIGN=MIDDLE  ALT=\"x=1-3i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In sum, the four roots of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-6x%5E3%2B71x%5E2-146x%2B530=0 ALIGN=MIDDLE  ALT=\"x%5E4-6x%5E3%2B71x%5E2-146x%2B530=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B7i ALIGN=MIDDLE  ALT=\"2%2B7i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-7i ALIGN=MIDDLE  ALT=\"2-7i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B3i ALIGN=MIDDLE  ALT=\"1%2B3i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-3i ALIGN=MIDDLE  ALT=\"1-3i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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