document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=419087>Question 419087</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ust the value of the discriminant to determine the number and type of roots for x^2-4x=21 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #293142 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=293142\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the value of the discriminant to determine the number and type of roots for x^2-4x=21<BR>\n" );
document.write( "..<BR>\n" );
document.write( "x^2-4x=21<BR>\n" );
document.write( "x^2-4x-21=0<BR>\n" );
document.write( "a=1, b=-4, c=-21<BR>\n" );
document.write( "Discriminant=b^2-4*a*c<BR>\n" );
document.write( "=(-4)^2*-4*1*-21<BR>\n" );
document.write( "=16+84=100>0<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "Function has two real roots.<BR>\n" );
document.write( "Note: because discriminant is a perfect square in this case, function is factorable like:<BR>\n" );
document.write( "(x-7)(x+3)=0<BR>\n" );
document.write( "See graph of function below:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-30%2C+30%2C+x%5E2-4x-21%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-30%2C+30%2C+x%5E2-4x-21%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );