document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130949>Question 130949</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve.\r<BR>\n" );
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document.write( "w^4-12w^2-2=0\r<BR>\n" );
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document.write( "I did a similar problem and was supposed to come up with 4 different radicals and I only came up with 2 for my answer and was told it was wrong. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #95551 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=95551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E4-12w%5E2-2=0 ALIGN=MIDDLE  ALT=\"w%5E4-12w%5E2-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=w%5E2 ALIGN=MIDDLE  ALT=\"u=w%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2-12u-2=0 ALIGN=MIDDLE  ALT=\"u%5E2-12u-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Complete the square:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2-12u%2B36=38 ALIGN=MIDDLE  ALT=\"u%5E2-12u%2B36=38\"   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=%28u-6%29%5E2=38 ALIGN=MIDDLE  ALT=\"%28u-6%29%5E2=38\"   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=u-6=sqrt%2838%29 ALIGN=MIDDLE  ALT=\"u-6=sqrt%2838%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u-6=-sqrt%2838%29 ALIGN=MIDDLE  ALT=\"u-6=-sqrt%2838%29\"   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=u%5B1%5D=6%2Bsqrt%2838%29 ALIGN=MIDDLE  ALT=\"u%5B1%5D=6%2Bsqrt%2838%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5B2%5D=6-sqrt%2838%29 ALIGN=MIDDLE  ALT=\"u%5B2%5D=6-sqrt%2838%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=w%5E2 ALIGN=MIDDLE  ALT=\"u=w%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=sqrt%28u%29 ALIGN=MIDDLE  ALT=\"w=sqrt%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-sqrt%28u%29 ALIGN=MIDDLE  ALT=\"w=-sqrt%28u%29\"   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=w=sqrt%28u%5B1%5D%29=sqrt%286%2Bsqrt%2838%29%29 ALIGN=MIDDLE  ALT=\"w=sqrt%28u%5B1%5D%29=sqrt%286%2Bsqrt%2838%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=sqrt%28u%5B2%5D%29=sqrt%286-sqrt%2838%29%29 ALIGN=MIDDLE  ALT=\"w=sqrt%28u%5B2%5D%29=sqrt%286-sqrt%2838%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-sqrt%28u%5B1%5D%29=-sqrt%286%2Bsqrt%2838%29%29 ALIGN=MIDDLE  ALT=\"w=-sqrt%28u%5B1%5D%29=-sqrt%286%2Bsqrt%2838%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-sqrt%28u%5B2%5D%29=-sqrt%286-sqrt%2838%29%29 ALIGN=MIDDLE  ALT=\"w=-sqrt%28u%5B2%5D%29=-sqrt%286-sqrt%2838%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Anytime you have a 4th degree polynomial equation, you must expect to have exactly 4 roots.  They may be 4 real roots, 2 pairs of complex congujate roots, or 2 real roots and 1 pair of complex conjugate roots.  Pairs of real roots might be identical (multiplicity greater than 1) but there will ALWAYS be 4 roots when the highest degree term is 4. </SPAN>\n" );
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