document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=18077>Question 18077</A>: <I><SPAN STYLE=\"word-break: break-all;\">  p(x)=4x^3-16x^2+21x-27 has three real roots one of them is 3 and a conjugate complex pair of roots which is _____ +- _____i <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #8724 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=8724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p(x)=4x^3-16x^2+21x-27 has three real roots one of them is 3 and a conjugate complex pair of roots which is _____ +- _____i <BR>\n" );
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document.write( "the wording of the problem is not correct ...to say the eqn. has 3 real roots<BR>\n" );
document.write( "and then ask for conjugate complex pair of roots which is _____ +- _____i <BR>\n" );
document.write( "ANY WAY LET US SOLVE AND SEE...\r<BR>\n" );
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document.write( "since 3 is a root x-3 is a factor.let us divide with x-3 using short division.<BR>\n" );
document.write( "3..|..4....-16....21....-27<BR>\n" );
document.write( "...|..0.....12....-12....27<BR>\n" );
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document.write( "......4....-4.....9......0 is remainder<BR>\n" );
document.write( " 4x^2-4x+9=0...using the formula for roots of ax^2+bx+c=0 ,we have...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A4%2A9+%29%29%2F%282%2A4%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A4%2A9+%29%29%2F%282%2A4%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+=+%284+%2B-+sqrt%28+16-144%29%29%2F%288%29+ ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+sqrt%28+16-144%29%29%2F%288%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+=+%284%2B-+sqrt%28-128%29%29%2F%288%29+ ALIGN=MIDDLE  ALT=\"x+=+%284%2B-+sqrt%28-128%29%29%2F%288%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+=+%284%2B-8sqrt%28-2%29%29%2F%288%29+ ALIGN=MIDDLE  ALT=\"x+=+%284%2B-8sqrt%28-2%29%29%2F%288%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+=+%284%2F8%29%2B-sqrt%28-2%29%29 ALIGN=MIDDLE  ALT=\"x+=+%284%2F8%29%2B-sqrt%28-2%29%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=%281%2F2%29%2Bi%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"x=%281%2F2%29%2Bi%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...and..<BR>\n" );
document.write( "..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2F2%29-i%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"x=%281%2F2%29-i%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...\r<BR>\n" );
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