document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184307>Question 1184307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that the equation px^2 + 3px + p + q = 0,where p is not = 0, has two equal real roots,find q in terms 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 #814856 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=814856\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Given that the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=px%5E2+%2B+3px+%2B+p+%2B+q+=+0 ALIGN=MIDDLE  ALT=\"px%5E2+%2B+3px+%2B+p+%2B+q+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+%3C%3E+0 ALIGN=MIDDLE  ALT=\"p+%3C%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, has two equal real roots, find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q ALIGN=MIDDLE  ALT=\"q\"   DISABLED_style= \"max-width:90%; height:auto;\" > in terms 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( " the equation has two equal real roots if discriminant is equal to zero\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=px%5E2+%2B+3px+%2B+p+%2B+q+=+0 ALIGN=MIDDLE  ALT=\"px%5E2+%2B+3px+%2B+p+%2B+q+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > in your case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=p ALIGN=MIDDLE  ALT=\"a=p\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3p ALIGN=MIDDLE  ALT=\"b=3p\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=+p+%2B+q+ ALIGN=MIDDLE  ALT=\"c=+p+%2B+q+\"   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=%283p%29%5E2-4%2Ap%2A%28p+%2B+q%29=0 ALIGN=MIDDLE  ALT=\"%283p%29%5E2-4%2Ap%2A%28p+%2B+q%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=9p%5E2-+%284p%5E2+%2B+4pq%29=0 ALIGN=MIDDLE  ALT=\"9p%5E2-+%284p%5E2+%2B+4pq%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=9p%5E2-+4pq-+4p%5E2=0 ALIGN=MIDDLE  ALT=\"9p%5E2-+4pq-+4p%5E2=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=5p%5E2-+4pq=0 ALIGN=MIDDLE  ALT=\"5p%5E2-+4pq=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+%285p+-+4q%29+=+0 ALIGN=MIDDLE  ALT=\"p+%285p+-+4q%29+=+0\"   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=0 ALIGN=MIDDLE  ALT=\"p=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> exclude because gien that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+%3C%3E+0 ALIGN=MIDDLE  ALT=\"p+%3C%3E+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+-+4q%29+=+0 ALIGN=MIDDLE  ALT=\"%285p+-+4q%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5p+=+4q ALIGN=MIDDLE  ALT=\"5p+=+4q\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5p+=4q ALIGN=MIDDLE  ALT=\"5p+=4q\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=%285%2F4%29p++ ALIGN=MIDDLE  ALT=\"q=%285%2F4%29p++\"   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=px%5E2+%2B+3px+%2B+p+%2B+q+=+0 ALIGN=MIDDLE  ALT=\"px%5E2+%2B+3px+%2B+p+%2B+q+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=%285%2F4%29p+ ALIGN=MIDDLE  ALT=\"q=%285%2F4%29p+\"   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=px%5E2+%2B+3px+%2B+p+%2B+%285%2F4%29p+=+0 ALIGN=MIDDLE  ALT=\"px%5E2+%2B+3px+%2B+p+%2B+%285%2F4%29p+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....both sides multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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=4px%5E2+%2B+12px+%2B+4p+%2B+5p+=+0 ALIGN=MIDDLE  ALT=\"4px%5E2+%2B+12px+%2B+4p+%2B+5p+=+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=4px%5E2+%2B+12px+%2B+9p+=+0 ALIGN=MIDDLE  ALT=\"4px%5E2+%2B+12px+%2B+9p+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check if discriminant is equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812p%29%5E2-4%284p%29%289p%29=0 ALIGN=MIDDLE  ALT=\"%2812p%29%5E2-4%284p%29%289p%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=144p%5E2-144p%5E2=0 ALIGN=MIDDLE  ALT=\"144p%5E2-144p%5E2=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=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>true\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );