document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=976056>Question 976056</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the roots of the polynomial<BR>\n" );
document.write( "p(x) = x^4+4x^3+6x^2+4x+5=0 given that one of the roots is x= -i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597753 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39627)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=597753\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Another root is x=i, because complex roots for polynomial functions come as conjugate pairs.  Those two roots are as  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%28-i%29%29%28x-i%29=%28x-i%29%28x%2Bi%29 ALIGN=MIDDLE  ALT=\"%28x-%28-i%29%29%28x-i%29=%28x-i%29%28x%2Bi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-i%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%28-1%29 ALIGN=MIDDLE  ALT=\"x%5E2-%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a factor of the polynomial p(x).\r<BR>\n" );
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document.write( "Use polynomial division for   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4%2B4x%5E3%2B6x%5E2%2B4x%2B5 ALIGN=MIDDLE  ALT=\"x%5E4%2B4x%5E3%2B6x%5E2%2B4x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > as dividend<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B1 ALIGN=MIDDLE  ALT=\"x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  as divisor.  The quotient represents the rest of the factors, as quadratic, degree two.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "The division process not shown here; but result is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x%2B5 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the quotient.\r<BR>\n" );
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document.write( "Use general solution method for a quadratic equation to find the zeros of this factor:<BR>\n" );
document.write( "roots are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-4%2B-+sqrt%284%5E2-4%2A5%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-4%2B-+sqrt%284%5E2-4%2A5%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-4%2B-+sqrt%28-4%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-4%2B-+sqrt%28-4%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=x=%28-4%2B-+2i%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-4%2B-+2i%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-2%2B-+i%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-2%2B-+i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   or   -2-i  and  -2+i.\r<BR>\n" );
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document.write( "(along with  -i  and i ). </SPAN>\n" );
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