document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95598>Question 95598</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0073016020/algebrahomeworkh>Beginning Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me tonight with this problem?  \r<BR>\n" );
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document.write( "Find all positive values for k for which each of the following can be factored.  \r<BR>\n" );
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document.write( "x^2 + x - k \r<BR>\n" );
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document.write( "Thanks for your help.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69638 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=69638\">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" );
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document.write( "That depends on what restrictions there are on the factors.<BR>\n" );
document.write( "Actually every quadratic can be factored; the quadratic <BR>\n" );
document.write( "equation quarantees that.<BR>\n" );
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document.write( "I'm going to assume your question means \"factor in the Real <BR>\n" );
document.write( "Number System\".<BR>\n" );
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document.write( "In that case b^2-4ac must be greater than or equal to zero:<BR>\n" );
document.write( "x^2 + x - k \r<BR>\n" );
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document.write( "b^2-4ac = 1^2-4*1*-k = 1+4k must be >=0<BR>\n" );
document.write( "1-4k>=0<BR>\n" );
document.write( "4k<=1<BR>\n" );
document.write( "k<=1/4<BR>\n" );
document.write( "As long as k<=1/4 the quadratic will have Real Number<BR>\n" );
document.write( "roots and will have factors with Real Numbers.<BR>\n" );
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document.write( "That is the best answer I can come up with.  If you have <BR>\n" );
document.write( "more information regarding the problem, post it again with<BR>\n" );
document.write( "the additional information.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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