document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=234850>Question 234850</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am just not understanding these type of problems. For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary to find the roots; just determine the number and types of solutions.\r<BR>\n" );
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document.write( "z^2+z+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 #173268 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=173268\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary to find the roots; just determine the number and types of solutions.<BR>\n" );
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document.write( "You have to know the rules of the discriminate<BR>\n" );
document.write( "we are talking about the quadratic form y = ax^2 = bx + c<BR>\n" );
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document.write( "The discriminate formula<BR>\n" );
document.write( "d = b^2 - 4 * a * c<BR>\n" );
document.write( "If d is positive: two real roots<BR>\n" );
document.write( "If d = 0: two equal and real roots<BR>\n" );
document.write( "If d = less than 0, (neg) no real roots, (complex)<BR>\n" );
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document.write( "z^2 + z + 1<BR>\n" );
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document.write( "In this problem<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = 1<BR>\n" );
document.write( "c = 1<BR>\n" );
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document.write( "The discriminate<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E2+-+4+%2A+1+%2A+1 ALIGN=MIDDLE  ALT=\"1%5E2+-+4+%2A+1+%2A+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = 1 - 4<BR>\n" );
document.write( "d = -3, negative, no real roots, complex<BR>\n" );
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