document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144707>Question 144707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the discriminant of a complete quadratic equation is 8, what is the nature of its root?<BR>\n" );
document.write( "A. Imaginary and identical<BR>\n" );
document.write( "B. Imaginary and Unequal<BR>\n" );
document.write( "C. Real and identical<BR>\n" );
document.write( "D. Real and unequal </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105446 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=105446\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the discriminant, i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   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=D%3C0 ALIGN=MIDDLE  ALT=\"D%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the roots are a conjugate pair of complex numbers of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha%2B-beta%2Ai ALIGN=MIDDLE  ALT=\"alpha%2B-beta%2Ai\"   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=D=0 ALIGN=MIDDLE  ALT=\"D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the roots are real and equal.  (Also described as a single root with a multiplicity of 2)\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%3E0 ALIGN=MIDDLE  ALT=\"D%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the roots are real and unequal.\r<BR>\n" );
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document.write( "Note that choice A is never possible, and choice B only occurs when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > equals 0 so that the complex roots become <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B-beta%2Ai ALIGN=MIDDLE  ALT=\"0%2B-beta%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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