document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=97701>Question 97701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all positive values for k for which each of the following can be factored.<BR>\n" );
document.write( "x^2+x-k\r<BR>\n" );
document.write( "\n" );
document.write( "I've tried everything and it just isn't making sense to me since there are no numbers to factor. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #71082 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=71082\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find all positive values for k for which each of the following can be factored.<BR>\n" );
document.write( "x^2+x-k<BR>\n" );
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document.write( "If you make the assumption that the factoring is limited to the <BR>\n" );
document.write( "Real Number System, then b^2-4ac must be greater than or equal <BR>\n" );
document.write( "to zero.<BR>\n" );
document.write( "Your Problem:<BR>\n" );
document.write( "a=1, b=1, c=k<BR>\n" );
document.write( "b^2-4ac = 1-4k>=0<BR>\n" );
document.write( "4k<=1`<BR>\n" );
document.write( "k<=(1/4)<BR>\n" );
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document.write( "As long as k<=(1/4) the quadratic will be factorable<BR>\n" );
document.write( "in the Real Number System.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );