document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997509>Question 997509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the values of p for which (7p+1)x^2+(5p-1)x+p=1 has equal roots...<BR>\n" );
document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615579 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=615579\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the values of p for which <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287p%2B1%29x%5E2%2B%285p-1%29x%2Bp=1 ALIGN=MIDDLE  ALT=\"%287p%2B1%29x%5E2%2B%285p-1%29x%2Bp=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > has equal roots\r<BR>\n" );
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document.write( "For the quadratic equation to have equal roots, the argument to the square root must equal zero and the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b+%2F+2a ALIGN=MIDDLE  ALT=\"-b+%2F+2a\"   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=%287p%2B1%29x%5E2%2B%285p-1%29x%2Bp=1 ALIGN=MIDDLE  ALT=\"%287p%2B1%29x%5E2%2B%285p-1%29x%2Bp=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287p%2B1%29x%5E2%2B%285p-1%29x%2Bp-1=0 ALIGN=MIDDLE  ALT=\"%287p%2B1%29x%5E2%2B%285p-1%29x%2Bp-1=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+=+0+ ALIGN=MIDDLE  ALT=\"b%5E2+-+4ac+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%287p%2B1%29 ALIGN=MIDDLE  ALT=\"a=%287p%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%285p-1%29 ALIGN=MIDDLE  ALT=\"b=%285p-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=p-1 ALIGN=MIDDLE  ALT=\"c=p-1\"   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+=+0 ALIGN=MIDDLE  ALT=\"b%5E2+-4ac+=+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=%285p-1%29%5E2+-4%287p%2B1%29%28p-1%29+=+0 ALIGN=MIDDLE  ALT=\"%285p-1%29%5E2+-4%287p%2B1%29%28p-1%29+=+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=25p%5E2+-10p%2B1-%2828p%5E2+%2B4%29%28p-1%29+=+0 ALIGN=MIDDLE  ALT=\"25p%5E2+-10p%2B1-%2828p%5E2+%2B4%29%28p-1%29+=+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=25p%5E2+-10p%2B1-%2828p%5E3-28p%5E2%2B4p-4%29+=+0 ALIGN=MIDDLE  ALT=\"25p%5E2+-10p%2B1-%2828p%5E3-28p%5E2%2B4p-4%29+=+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=25p%5E2+-10p%2B1-28p%5E3%2B28p%5E2-4p%2B4+=+0 ALIGN=MIDDLE  ALT=\"25p%5E2+-10p%2B1-28p%5E3%2B28p%5E2-4p%2B4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3p%5E2%2B14p%2B5+=+0 ALIGN=MIDDLE  ALT=\"-3p%5E2%2B14p%2B5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........using quadratic formula, you have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"p=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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=p=+%28-14+%2B-+sqrt%28+14%5E2-4%2A%28-3%29%2A5+%29%29%2F%282%2A%28-3%29%29+ ALIGN=MIDDLE  ALT=\"p=+%28-14+%2B-+sqrt%28+14%5E2-4%2A%28-3%29%2A5+%29%29%2F%282%2A%28-3%29%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=p=+%28-14+%2B-+sqrt%28+196%2B60+%29%29%2F-6+ ALIGN=MIDDLE  ALT=\"p=+%28-14+%2B-+sqrt%28+196%2B60+%29%29%2F-6+\"   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=p=+%28-14+%2B-+sqrt%28+256+%29%29%2F-6+ ALIGN=MIDDLE  ALT=\"p=+%28-14+%2B-+sqrt%28+256+%29%29%2F-6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=+%28-14+%2B-+16%29%2F-6+ ALIGN=MIDDLE  ALT=\"p=+%28-14+%2B-+16%29%2F-6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=+%28-cross%2814%297+%2B-+cross%2816%298%29%2Fcross%28-6%29-33+ ALIGN=MIDDLE  ALT=\"p=+%28-cross%2814%297+%2B-+cross%2816%298%29%2Fcross%28-6%29-33+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=+%28-7+%2B-+8%29%2F-3+ ALIGN=MIDDLE  ALT=\"p=+%28-7+%2B-+8%29%2F-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >    \r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=+%28-7+%2B+8%29%2F-3+ ALIGN=MIDDLE  ALT=\"p=+%28-7+%2B+8%29%2F-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=+-1%2F3+ ALIGN=MIDDLE  ALT=\"p=+-1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=+%28-7+-+8%29%2F-3+ ALIGN=MIDDLE  ALT=\"p=+%28-7+-+8%29%2F-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=+-15%2F-3+ ALIGN=MIDDLE  ALT=\"p=+-15%2F-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=+5 ALIGN=MIDDLE  ALT=\"p=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then your equation will be\r<BR>\n" );
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document.write( "if<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+=-1%2F3 ALIGN=MIDDLE  ALT=\"+p+=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%28-1%2F3%29%2B1%29x%5E2%2B%285%28-1%2F3%29-1%29x%2B%28-1%2F3%29-1=0 ALIGN=MIDDLE  ALT=\"%287%28-1%2F3%29%2B1%29x%5E2%2B%285%28-1%2F3%29-1%29x%2B%28-1%2F3%29-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-7%2F3%2B3%2F3%29x%5E2%2B%28-5%2F3-3%2F3%29x-1%2F3-3%2F3=0 ALIGN=MIDDLE  ALT=\"%28-7%2F3%2B3%2F3%29x%5E2%2B%28-5%2F3-3%2F3%29x-1%2F3-3%2F3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%284%2F3%29x%5E2-%288%2F3%29x-4%2F3=0 ALIGN=MIDDLE  ALT=\"-%284%2F3%29x%5E2-%288%2F3%29x-4%2F3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > => this works, gives us one  root\r<BR>\n" );
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document.write( "check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-%284%2F3%29x%5E2-%288%2F3%29x-4%2F3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-%284%2F3%29x%5E2-%288%2F3%29x-4%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "or\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=5 ALIGN=MIDDLE  ALT=\"p+=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%285%29%2B1%29x%5E2%2B%285%285%29-1%29x%2B5-1=0 ALIGN=MIDDLE  ALT=\"%287%285%29%2B1%29x%5E2%2B%285%285%29-1%29x%2B5-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x%5E2%2B24x%2B4=0 ALIGN=MIDDLE  ALT=\"36x%5E2%2B24x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> this works, gives us one  root\r<BR>\n" );
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document.write( "<BR>\n" );
document.write( "\n" );
document.write( "check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-5%2C+5%2C+-10%2C+10%2C+36x%5E2%2B24x%2B4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-5%2C+5%2C+-10%2C+10%2C+36x%5E2%2B24x%2B4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );