document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=469726>Question 469726</A>: <I><SPAN STYLE=\"word-break: break-all;\"> help please\r<BR>\n" );
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document.write( "Use the discriminant to determine the number of real solutions of the equation.<BR>\n" );
document.write( "5x^2-3x+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 #322239 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=322239\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The discriminant, D is as follows:<BR>\n" );
document.write( "given quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "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;\" ><BR>\n" );
document.write( "If D = 0, then there is only 1 real solution, specifically x = -b/2a<BR>\n" );
document.write( "If D > 0, then there are exactly 2 real solutions<BR>\n" );
document.write( "If D < 0, then no real solutions exist, graph never crosses x-axis<BR>\n" );
document.write( "For this equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+-+3x+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"5x%5E2+-+3x+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 5<BR>\n" );
document.write( "b = -3<BR>\n" );
document.write( "c = 1<BR>\n" );
document.write( "D = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%5E2+-+4%285%29%281%29 ALIGN=MIDDLE  ALT=\"%28-3%29%5E2+-+4%285%29%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+-+20 ALIGN=MIDDLE  ALT=\"9+-+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11 ALIGN=MIDDLE  ALT=\"-11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-11 < 0<BR>\n" );
document.write( "Therefore, no real solutions exist for this equation </SPAN>\n" );
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