document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=674271>Question 674271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a third-degree polynomial equation with rational coefficients that has roots –4 and 6 + i.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #419690 by </B><A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><B>ReadingBoosters(3246)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><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=419690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given roots<BR>\n" );
document.write( "-4 and 6+i<BR>\n" );
document.write( "Inferred root 6-i (conjugate pair of 6+i)<BR>\n" );
document.write( "...<BR>\n" );
document.write( "x = -4<BR>\n" );
document.write( "x + 4 = 0<BR>\n" );
document.write( "(x+4)<BR>\n" );
document.write( "...<BR>\n" );
document.write( "x = 6 + i<BR>\n" );
document.write( "x - 6 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"sqrt%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=%28x-6%29%5E2+=+-1 ALIGN=MIDDLE  ALT=\"%28x-6%29%5E2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%5E2+%2B+1+=+0%0D%0A...%0D%0A%7B%7B%7B%28x%2B4%29%28x-6%29%5E2+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"%28x-6%29%5E2+%2B+1+=+0%0D%0A...%0D%0A%7B%7B%7B%28x%2B4%29%28x-6%29%5E2+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x%5E2-12x%2B36%29+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x%5E2-12x%2B36%29+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+12x%5E2+%2B+36x+%2B+4x%5E2+-+48x+%2B+144+%2B1+=+0 ALIGN=MIDDLE  ALT=\"x%5E3+-+12x%5E2+%2B+36x+%2B+4x%5E2+-+48x+%2B+144+%2B1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x%5E3+-+8x%5E2+-+12x+%2B+145=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x%5E3+-+8x%5E2+-+12x+%2B+145=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".....................<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );