document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=361774>Question 361774</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help with this problem:  Show that there is no quadratic equation ax^2 + bx + c = 0 such that a, b, and c are real numbers and 3i and -2i are solutions.\r<BR>\n" );
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document.write( "Thanks for your help.<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 #257862 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=257862\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3i ALIGN=MIDDLE  ALT=\"3i\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2i ALIGN=MIDDLE  ALT=\"-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > are solutions, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3i%29 ALIGN=MIDDLE  ALT=\"%28x-3i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2i%29 ALIGN=MIDDLE  ALT=\"%28x%2B2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are factors of the quadratic equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3i%29%28x%2B2i%29=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"%28x-3i%29%28x%2B2i%29=ax%5E2%2Bbx%2Bc\"   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%2B2ix-3ix-6i%5E2=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"x%5E2%2B2ix-3ix-6i%5E2=ax%5E2%2Bbx%2Bc\"   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%2B%28-3i%2B2i%29x%2B6=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"x%5E2%2B%28-3i%2B2i%29x%2B6=ax%5E2%2Bbx%2Bc\"   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-ix%2B6=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"x%5E2-ix%2B6=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Comparing<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-i ALIGN=MIDDLE  ALT=\"b=-i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=6 ALIGN=MIDDLE  ALT=\"c=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "However a,b, and c are supposed to be real. <BR>\n" );
document.write( "Therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3i ALIGN=MIDDLE  ALT=\"3i\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2i ALIGN=MIDDLE  ALT=\"-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be solutions where a,b, and c are real numbers. </SPAN>\n" );
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