document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184258>Question 1184258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the line y + 2x = p does not intersect the curve y^2 = x + p, find the range of values of p </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814810 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814810\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "If the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%2B+2x+=+p+ ALIGN=MIDDLE  ALT=\"y+%2B+2x+=+p+\"   DISABLED_style= \"max-width:90%; height:auto;\" >does not intersect the curve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+x+%2B+p ALIGN=MIDDLE  ALT=\"y%5E2+=+x+%2B+p\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find the range of values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   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=y+%2B+2x+=+p+ ALIGN=MIDDLE  ALT=\"y+%2B+2x+=+p+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+x+%2B+p ALIGN=MIDDLE  ALT=\"y%5E2+=+x+%2B+p\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........eq.2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+p+-2x ALIGN=MIDDLE  ALT=\"y+=+p+-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28p%2Bx%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28p%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........eq.2\r<BR>\n" );
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document.write( "=>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+-2x=+sqrt%28p%2Bx%29 ALIGN=MIDDLE  ALT=\"p+-2x=+sqrt%28p%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p+-2x%29%5E2=+%28sqrt%28p%2Bx%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28p+-2x%29%5E2=+%28sqrt%28p%2Bx%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2+-+4px+%2B+4x%5E2=+p%2Bx ALIGN=MIDDLE  ALT=\"p%5E2+-+4px+%2B+4x%5E2=+p%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2+-+4px+%2B+4x%5E2-+p-x=0 ALIGN=MIDDLE  ALT=\"p%5E2+-+4px+%2B+4x%5E2-+p-x=0\"   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=4x%5E2-+4px-x%2Bp%5E2++-+p=0 ALIGN=MIDDLE  ALT=\"4x%5E2-+4px-x%2Bp%5E2++-+p=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-+%284p%2B1%29x%2B%28p%5E2++-+p%29=0 ALIGN=MIDDLE  ALT=\"4x%5E2-+%284p%2B1%29x%2B%28p%5E2++-+p%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use discriminant<BR>\n" );
document.write( "the line will not intersect  the curve if\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac+%3C++0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac+%3C++0\"   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=b%5E2-4ac+%3C0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac+%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-+%284p%2B1%29 ALIGN=MIDDLE  ALT=\"b=-+%284p%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=%28p%5E2++-+p%29 ALIGN=MIDDLE  ALT=\"c=%28p%5E2++-+p%29\"   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=%28-+%284p%2B1%29%29%5E2-4%2A4%28p%5E2++-+p%29+%3C0 ALIGN=MIDDLE  ALT=\"%28-+%284p%2B1%29%29%5E2-4%2A4%28p%5E2++-+p%29+%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16p%5E2+%2B+8+p+%2B+1-16p%5E2++%2B16+p+%3C++0++ ALIGN=MIDDLE  ALT=\"16p%5E2+%2B+8+p+%2B+1-16p%5E2++%2B16+p+%3C++0++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8p+%2B+1+++%2B16p+%3C++0 ALIGN=MIDDLE  ALT=\"8p+%2B+1+++%2B16p+%3C++0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24p+++%2B1%3C0 ALIGN=MIDDLE  ALT=\"24p+++%2B1%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+%3C++-1%2F24+ ALIGN=MIDDLE  ALT=\"p+%3C++-1%2F24+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the line will not intersect  the curve if  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+%3C++-1%2F24+ ALIGN=MIDDLE  ALT=\"p+%3C++-1%2F24+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );