document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206552>Question 1206552</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What value of K will cause <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Kn%5E2+-+3n+%2B+2Kn+%2B+1 ALIGN=MIDDLE  ALT=\"Kn%5E2+-+3n+%2B+2Kn+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to have two zeroes / roots? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844113 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53751)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "This problem is a TRAP.\r<BR>\n" );
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document.write( "The trap is in leading coefficient K at n^2.\r<BR>\n" );
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document.write( "A regular student does understand (and does know) that a quadratic equation <BR>\n" );
document.write( "has two roots, when the discriminant is different from 0 (from zero),\r<BR>\n" );
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document.write( "and has one root, if the discriminant is zero.\r<BR>\n" );
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document.write( "So, it is a standard expected answer.\r<BR>\n" );
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document.write( "But here the trap starts working.\r<BR>\n" );
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document.write( "All that I said above is correct if an equation is really quadratic.\r<BR>\n" );
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document.write( "But if K= 0, the equation is just NOT a quadratic - it is linear.\r<BR>\n" );
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document.write( "In this case, the quadratic formula does not work and is not applicable.\r<BR>\n" );
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document.write( "It is what a regular student usually misses - and therefore gets a reduced score at an exam.\r<BR>\n" );
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document.write( "So, in this problem bad (or special) values of K are those numbers (real or complex),<BR>\n" );
document.write( "that make the discriminant of the quadratic equation zero PLUS the value K= 0, <BR>\n" );
document.write( "which makes the quadratic equation degenerated and, actually, linear.\r<BR>\n" );
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document.write( "So, this problem is a (well known) tool in hands of some examinators, when they want \"to kill\" some students.\r<BR>\n" );
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document.write( "It is the knowledge that good student must know in order to avoid falling into this trap.\r<BR>\n" );
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document.write( "Thus, this my solution has a very practical outcome.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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