document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183695>Question 1183695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value of K for which y=x+k is a tangent to the curve y=x²+5x+2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814139 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814139\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Without using calculus, a simpler solution would be as follows:\r<BR>\n" );
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document.write( "Equate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+%2B+5x+%2B+2 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+%2B+5x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x+%2B+k ALIGN=MIDDLE  ALT=\"y+=+x+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+5x+%2B+2+=+x+%2B+k ALIGN=MIDDLE  ALT=\"x%5E2+%2B+5x+%2B+2+=+x+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since at their intersection point(s) they're supposed to have the same y-values.\r<BR>\n" );
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document.write( "<===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x+%2B+%282-k%29+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+%2B+%282-k%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since the line is supposed to be tangent to the curve, it means that there are two identical roots for the preceding equation.  \r<BR>\n" );
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document.write( "This only happens when the discriminant is equal to 0, i.e.,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2+-+4%2A1%2A%282-k%29+=+0 ALIGN=MIDDLE  ALT=\"4%5E2+-+4%2A1%2A%282-k%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2+=+4%282-k%29 ALIGN=MIDDLE  ALT=\"4%5E2+=+4%282-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k+=+-2%29 ALIGN=MIDDLE  ALT=\"highlight%28k+=+-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Solved. </SPAN>\n" );
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