document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=478945>Question 478945</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex.  Note: It is not necessary to find the roots; just determine the number and types of solutions.\r<BR>\n" );
document.write( "\n" );
document.write( "2x^2 - 10x + 25 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #328196 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=328196\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The discriminant is <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 the discriminant is 0, then the equation has a double solution, that is both solutions are identical and real. Many times this is called a \"single\" solution.<BR>\n" );
document.write( "If the discriminant is positive, then the equation has two real solutions.<BR>\n" );
document.write( "If the discriminant is negative, then the equation has two complex solutions.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-10x%2B25+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2-10x%2B25+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The discriminant is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-10%29%5E2-4%282%29%2825%29+=+100-200 ALIGN=MIDDLE  ALT=\"%28-10%29%5E2-4%282%29%2825%29+=+100-200\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-100 ALIGN=MIDDLE  ALT=\"-100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The discriminant is negative so there are two complex solutions. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );