document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177918>Question 177918</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate the discriminant of each equation. How many real and imaginary<BR>\n" );
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document.write( "37. x2 + 5x + 6 = 0 \r<BR>\n" );
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document.write( "38. 3x2 - 4x + 3 = 0\r<BR>\n" );
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document.write( "39. -2x2 - 5x + 4 = 0 \r<BR>\n" );
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document.write( "40. 16x2 - 8x + 1 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132896 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=132896\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  D=<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;\" >  where D is the discriminant<BR>\n" );
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document.write( "....zero, bē - 4ac = 0 ----->1 real (double)eg (x-3)(x-3) <BR>\n" );
document.write( "positive, bē - 4ac > 0 ----->2 real roots <BR>\n" );
document.write( "negative, bē - 4ac < 0 ----->2 complex roots <BR>\n" );
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document.write( "Equations taken in the form of ax+by+c=0<BR>\n" );
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document.write( "I will do one and let you complete the rest<BR>\n" );
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document.write( "37. x2 + 5x + 6 = 0 <BR>\n" );
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document.write( "a=1,b=5,c=6<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=5%5E2-4%28%281%29%286%29%29=25-24=1 ALIGN=MIDDLE  ALT=\"D=5%5E2-4%28%281%29%286%29%29=25-24=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >since D>0 we will have 2 real roots.\r<BR>\n" );
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document.write( "38. 3x2 - 4x + 3 = 0<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%5E2-4%283%29%283%29=16-36=-20 ALIGN=MIDDLE  ALT=\"%28-4%29%5E2-4%283%29%283%29=16-36=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >D<0<BR>\n" );
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document.write( "so 2 complex roots<BR>\n" );
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document.write( "39. -2x2 - 5x + 4 = 0<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%29%5E2-4%28-2%29%284%29=+25%2B32=57 ALIGN=MIDDLE  ALT=\"%28-5%29%5E2-4%28-2%29%284%29=+25%2B32=57\"   DISABLED_style= \"max-width:90%; height:auto;\" >D>0 so 2 real roots<BR>\n" );
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document.write( "40. 16x2 - 8x + 1 = 0<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-8%29%5E2-4%2816%29%281%29=64-64=0 ALIGN=MIDDLE  ALT=\"%28-8%29%5E2-4%2816%29%281%29=64-64=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >so 1 real (double) root\r<BR>\n" );
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document.write( " </SPAN>\n" );
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