document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=403541>Question 403541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello. I was hoping you could please help me? <BR>\n" );
document.write( "I need to solve this equation : \r<BR>\n" );
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document.write( "k^5+4k^4-32k^3=0\r<BR>\n" );
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document.write( "Since its highest degree is 5, my teacher said we should get 5 roots, but when I tried it, I only got 3 roots, which were: 0, -8, and 4<BR>\n" );
document.write( "Can you please show me the correct way to do it? I'm doing it by factoring... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #285332 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=285332\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E5%2B4k%5E4-32k%5E3=0+ ALIGN=MIDDLE  ALT=\"k%5E5%2B4k%5E4-32k%5E3=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=k%5E3%28k%5E2%2B4k-32%29=0+ ALIGN=MIDDLE  ALT=\"k%5E3%28k%5E2%2B4k-32%29=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....your equation will be equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E3=0 ALIGN=MIDDLE  ALT=\"k%5E3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%5E2%2B4k-32%29=0+ ALIGN=MIDDLE  ALT=\"%28k%5E2%2B4k-32%29=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, \r<BR>\n" );
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document.write( " if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E3=0 ALIGN=MIDDLE  ALT=\"k%5E3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...you have three roots, all of them are equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"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=k1=0 ALIGN=MIDDLE  ALT=\"k1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k2=0 ALIGN=MIDDLE  ALT=\"k2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k3=0 ALIGN=MIDDLE  ALT=\"k3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%5E2%2B4k-32%29=0+ ALIGN=MIDDLE  ALT=\"%28k%5E2%2B4k-32%29=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...here is quadratic, and it has two roots\r<BR>\n" );
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document.write( "use quadratic formula to find roots\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"k+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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=k+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A1%2A%28-32%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"k+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A1%2A%28-32%29+%29%29%2F%282%2A1%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=k+=+%28-4+%2B-+sqrt%2816+%2B128+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"k+=+%28-4+%2B-+sqrt%2816+%2B128+%29%29%2F2+\"   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=k+=+%28-4+%2B-+sqrt%28144+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"k+=+%28-4+%2B-+sqrt%28144+%29%29%2F2+\"   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=k+=+%28-4+%2B-+12%29%2F2+ ALIGN=MIDDLE  ALT=\"k+=+%28-4+%2B-+12%29%2F2+\"   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=k4+=+%28-4+%2B+12%29%2F2+ ALIGN=MIDDLE  ALT=\"k4+=+%28-4+%2B+12%29%2F2+\"   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=k4+=+8%2F2+ ALIGN=MIDDLE  ALT=\"k4+=+8%2F2+\"   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=k4+=+4+ ALIGN=MIDDLE  ALT=\"k4+=+4+\"   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=k5+=+%28-4+-+12%29%2F2+ ALIGN=MIDDLE  ALT=\"k5+=+%28-4+-+12%29%2F2+\"   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=k5+=+%28-16%29%2F2+ ALIGN=MIDDLE  ALT=\"k5+=+%28-16%29%2F2+\"   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=k5+=+-8 ALIGN=MIDDLE  ALT=\"k5+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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