document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151469>Question 151469</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a complex number system, any quadratic equation has either one or two solutions. (That is the T/F question)\r<BR>\n" );
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document.write( "I believe this is false because I thought they will always have 2 solutions but can someone explain if I am wrong? \r<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 #111345 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=111345\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It is TRUE.<BR>\n" );
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document.write( "Consider the quadratic equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a+ ALIGN=MIDDLE  ALT=\"+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that we get our TWO solutions of a quadratic from the +- portion.<BR>\n" );
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document.write( "Now, let's focus our attention on (the term after the +-):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28b%5E2+-+4ac%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28b%5E2+-+4ac%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that if:<BR>\n" );
document.write( "b^2 is EQUAL to 4ac we will be taking the square root of zero.  In this case,<BR>\n" );
document.write( "we will get only one solution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-b+%2B-+sqrt%280%29%29%2F2a+ ALIGN=MIDDLE  ALT=\"+%28-b+%2B-+sqrt%280%29%29%2F2a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F2a+ ALIGN=MIDDLE  ALT=\"+-b%2F2a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "As an example, consider this:<BR>\n" );
document.write( "x^2+2x+1 = 0<BR>\n" );
document.write( "factoring we get:<BR>\n" );
document.write( "(x+1)(x+1) = 0<BR>\n" );
document.write( "Notice that we ONLY have a single solution of:<BR>\n" );
document.write( "x = -1<BR>\n" );
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