document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119096>Question 119096</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For what value(s) of 'p' would the equation px^2 + (2p+1)x+p=0 have two non-real roots? I think it is p=-1/4 but I'm only guessing. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87217 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=87217\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  From the quadratic formula\r<BR>\n" );
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document.write( "the discriminant consists of all of the terms in the square root. So the discriminant is\r<BR>\n" );
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document.write( "the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic. \r<BR>\n" );
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document.write( "So let's find the discriminant for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=px%5E2+%2B+%282p%2B1%29x%2Bp ALIGN=MIDDLE  ALT=\"px%5E2+%2B+%282p%2B1%29x%2Bp\"   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=D=%282p%2B1%29%5E2-4%2Ap%2Ap ALIGN=MIDDLE  ALT=\"D=%282p%2B1%29%5E2-4%2Ap%2Ap\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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=2p%2B1 ALIGN=MIDDLE  ALT=\"b=2p%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=p ALIGN=MIDDLE  ALT=\"c=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=D=4p%5E2%2B4p%2B1-4p%5E2 ALIGN=MIDDLE  ALT=\"D=4p%5E2%2B4p%2B1-4p%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil and multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=4p%2B1 ALIGN=MIDDLE  ALT=\"D=4p%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Now since we want to have 2 non-real solutions, this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%3C0 ALIGN=MIDDLE  ALT=\"D%3C0\"   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=3p%2B1%3C0 ALIGN=MIDDLE  ALT=\"3p%2B1%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the discriminant less than zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%3C0-1 ALIGN=MIDDLE  ALT=\"4p%3C0-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 1 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%3C-1 ALIGN=MIDDLE  ALT=\"4p%3C-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%3C%28-1%29%2F%284%29 ALIGN=MIDDLE  ALT=\"p%3C%28-1%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4 to isolate p \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%3C-1%2F4 ALIGN=MIDDLE  ALT=\"p%3C-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "--------------------------------------------------------------\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%3C-1%2F4 ALIGN=MIDDLE  ALT=\"p%3C-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (which is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%3C-0.25 ALIGN=MIDDLE  ALT=\"p%3C-0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > in decimal form)\r<BR>\n" );
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document.write( "So you're on the right track, but you have to remember that values such as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-10 ALIGN=MIDDLE  ALT=\"p=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > work also since -10 is less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F4 ALIGN=MIDDLE  ALT=\"-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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