document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177575>Question 1177575</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The quadratic equation x² + kx + 36=0 has\r<BR>\n" );
document.write( "\n" );
document.write( "two different real roots. Find the set of possible values of k. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #806637 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</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=806637\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bkx%2B36+=+%28x%2Ba%29%28x%2Bb%29+=+x%5E2%2B%28a%2Bb%29x%2B36 ALIGN=MIDDLE  ALT=\"x%5E2%2Bkx%2B36+=+%28x%2Ba%29%28x%2Bb%29+=+x%5E2%2B%28a%2Bb%29x%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The product of a and b has to be 36.<br><BR>\n" );
document.write( "Choose any two numbers a and b whose product is 36; the sum (a+b) will be one of the possible values for k.<br><BR>\n" );
document.write( "One example: a=9, b=4; ab=36; a+b=13.  One possible value of k is 13.<br><BR>\n" );
document.write( "One more: a=-3, b=-12; ab=36; a+b=-15.  Another possible value of k is -15.<br><BR>\n" );
document.write( "Note the statement of the problem is not complete; with no restriction on the values of a and b, there are an infinite number of possible values of k.  For example...<br><BR>\n" );
document.write( "a=8, b=4.5; ab=36; a+b=12.5; another possible value of k is 12.5.<br><BR>\n" );
document.write( "From that example, you can see that you could choose ANY value for a; then b would be 36/a, and you would get another value for a+b.<br><BR>\n" );
document.write( "So undoubtedly the question was supposed to ask for the set of possible INTEGER values of k.<br><BR>\n" );
document.write( "I'll let you finish the problem; you should find 18 different possible integer values for k.<br><BR>\n" );
document.write( "Note that two of those 18 values of k will be 12 and -12, where the a and b are both 6 or both -6.  Since the problem says the roots are different, you should find 16 different integer values of k in which the two roots are different.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );