document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178355>Question 1178355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation x^2+ax+b=0, where a and b are different, has solutions x=a, x=b. <BR>\n" );
document.write( "How many such equations are there? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807581 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=807581\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "In the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bax%2Bb=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bax%2Bb=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the sum of the roots is -a and the product of the roots is b.<br><BR>\n" );
document.write( "Then, since the roots are a and b...<br><BR>\n" );
document.write( "(1) a+b=-a<BR>\n" );
document.write( "(2) ab = b<br><BR>\n" );
document.write( "Equation (2) tells us a=1; then equation (1) tells us 1+b=-1 so b=-2.<br><BR>\n" );
document.write( "ANSWER: There is only one such equation:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx-2=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which has roots 1 and -2.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );