document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=955784>Question 955784</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if one root of the equation (p^2+2)x^2+7x+3p=0 is the reciprocal of the another then find the value of p<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #583884 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=583884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > be one root. Then the other root will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fr ALIGN=MIDDLE  ALT=\"1%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Consequently, their product will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%29%2A%281%2Fr%29+=+1 ALIGN=MIDDLE  ALT=\"%28r%29%2A%281%2Fr%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is true if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is nonzero.\r<BR>\n" );
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document.write( "Now, let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28p%5E2%2B2%29x%5E2%2B7x%2B3p=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28p%5E2%2B2%29x%5E2%2B7x%2B3p=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >. => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28p%5E2%2B2%29 ALIGN=MIDDLE  ALT=\"a=%28p%5E2%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=7 ALIGN=MIDDLE  ALT=\"b=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c=3p ALIGN=MIDDLE  ALT=\"+c=3p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+0 ALIGN=MIDDLE  ALT=\"f%28x%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then we are given that the roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fr ALIGN=MIDDLE  ALT=\"1%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "since product of roots is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c%2Fa=1 ALIGN=MIDDLE  ALT=\"+c%2Fa=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Fa=3p%2F%28p%5E2%2B2%29=1 ALIGN=MIDDLE  ALT=\"c%2Fa=3p%2F%28p%5E2%2B2%29=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=3p=1%2A%28p%5E2%2B2%29 ALIGN=MIDDLE  ALT=\"3p=1%2A%28p%5E2%2B2%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=0=p%5E2-3p%2B2 ALIGN=MIDDLE  ALT=\"0=p%5E2-3p%2B2\"   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=p%5E2-2p-p%2B2 ALIGN=MIDDLE  ALT=\"0=p%5E2-2p-p%2B2\"   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=%28p%5E2-2p%29-%28p-2%29 ALIGN=MIDDLE  ALT=\"0=%28p%5E2-2p%29-%28p-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=p%28p-2%29-%28p-2%29 ALIGN=MIDDLE  ALT=\"0=p%28p-2%29-%28p-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28p-1%29%28p-2%29 ALIGN=MIDDLE  ALT=\"0=%28p-1%29%28p-2%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=highlight%28p=1%29+ ALIGN=MIDDLE  ALT=\"highlight%28p=1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=2%29+ ALIGN=MIDDLE  ALT=\"highlight%28p=2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since SUM OF THE ROOTS is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+%2B+1%2Fr+=+-b%2Fa ALIGN=MIDDLE  ALT=\"+r+%2B+1%2Fr+=+-b%2Fa\"   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=+r+%2B+1%2Fr+=+-7%2F%28p%5E2%2B2%29 ALIGN=MIDDLE  ALT=\"+r+%2B+1%2Fr+=+-7%2F%28p%5E2%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Computing for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >: \r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=1%29+ ALIGN=MIDDLE  ALT=\"highlight%28p=1%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=+r+%2B+1%2Fr+=+-7%2F%281%5E2%2B2%29 ALIGN=MIDDLE  ALT=\"+r+%2B+1%2Fr+=+-7%2F%281%5E2%2B2%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=+%28r%5E2+%2B+1%29%2Fr+=+-7%2F3 ALIGN=MIDDLE  ALT=\"+%28r%5E2+%2B+1%29%2Fr+=+-7%2F3\"   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=+3%28r%5E2+%2B+1%29+=+-7r ALIGN=MIDDLE  ALT=\"+3%28r%5E2+%2B+1%29+=+-7r\"   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=+3r%5E2+%2B+3=+-7r ALIGN=MIDDLE  ALT=\"+3r%5E2+%2B+3=+-7r\"   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=+3r%5E2+%2B7r%2B+3=+0 ALIGN=MIDDLE  ALT=\"+3r%5E2+%2B7r%2B+3=+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=r+=+%281%2F6%29+%28sqrt%2813%29-7%29 ALIGN=MIDDLE  ALT=\"r+=+%281%2F6%29+%28sqrt%2813%29-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%281%2F6%29+%28-7-sqrt%2813%29%29 ALIGN=MIDDLE  ALT=\"r+=+%281%2F6%29+%28-7-sqrt%2813%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29+%28sqrt%2813%29-7%29+=+1%2F%28%281%2F6%29+%28-7-sqrt%2813%29%29%29 ALIGN=MIDDLE  ALT=\"%281%2F6%29+%28sqrt%2813%29-7%29+=+1%2F%28%281%2F6%29+%28-7-sqrt%2813%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-roots are reciprocal to each other\r<BR>\n" );
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document.write( "Thus, the actual roots are:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1+%5D=+%281%2F6%29+%28sqrt%2813%29-7%29+ ALIGN=MIDDLE  ALT=\"r%5B1+%5D=+%281%2F6%29+%28sqrt%2813%29-7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2+%5D=+%281%2F6+%29%28-7-sqrt%2813%29%29 ALIGN=MIDDLE  ALT=\"r%5B2+%5D=+%281%2F6+%29%28-7-sqrt%2813%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "second solution:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=2%29+ ALIGN=MIDDLE  ALT=\"highlight%28p=2%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=+r+%2B+1%2Fr+=+-7%2F%282%5E2%2B2%29 ALIGN=MIDDLE  ALT=\"+r+%2B+1%2Fr+=+-7%2F%282%5E2%2B2%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=+%28r%5E2+%2B+1%29%2Fr+=+-7%2F6 ALIGN=MIDDLE  ALT=\"+%28r%5E2+%2B+1%29%2Fr+=+-7%2F6\"   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=+6%28r%5E2+%2B+1%29+=+-7r ALIGN=MIDDLE  ALT=\"+6%28r%5E2+%2B+1%29+=+-7r\"   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=+6r%5E2+%2B+6=+-7r ALIGN=MIDDLE  ALT=\"+6r%5E2+%2B+6=+-7r\"   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=+6r%5E2+%2B7r%2B+6=+0 ALIGN=MIDDLE  ALT=\"+6r%5E2+%2B7r%2B+6=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...solving this using quadratic formula you will get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+%5B1%5D=+-%281%2F12%29%2Ai%28sqrt%2895%29-7i%29 ALIGN=MIDDLE  ALT=\"r+%5B1%5D=+-%281%2F12%29%2Ai%28sqrt%2895%29-7i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D+=+%281%2F12%29%2Ai+%28sqrt%2895%29%2B7i%29 ALIGN=MIDDLE  ALT=\"r%5B2%5D+=+%281%2F12%29%2Ai+%28sqrt%2895%29%2B7i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+%5B1%5D=1%2Fr+%5B2%5D ALIGN=MIDDLE  ALT=\"r+%5B1%5D=1%2Fr+%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F12%29%2Ai+%28sqrt%2895%29-7i%29=1%2F%28%281%2F12%29%2Ai+%28sqrt%2895%29%2B7i%29%29+ ALIGN=MIDDLE  ALT=\"-%281%2F12%29%2Ai+%28sqrt%2895%29-7i%29=1%2F%28%281%2F12%29%2Ai+%28sqrt%2895%29%2B7i%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check our function: if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=1%29+ ALIGN=MIDDLE  ALT=\"highlight%28p=1%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=%28p%5E2%2B2%29x%5E2%2B7x%2B3p=0 ALIGN=MIDDLE  ALT=\"%28p%5E2%2B2%29x%5E2%2B7x%2B3p=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%5E2%2B2%29x%5E2%2B7x%2B3%2A1=0 ALIGN=MIDDLE  ALT=\"%281%5E2%2B2%29x%5E2%2B7x%2B3%2A1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B7x%2B3=0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B7x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "roots are: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281%2F6%29+%28sqrt%2813%29-7%29 ALIGN=MIDDLE  ALT=\"x+=+%281%2F6%29+%28sqrt%2813%29-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281%2F6%29+%28-7-sqrt%2813%29%29 ALIGN=MIDDLE  ALT=\"x+=+%281%2F6%29+%28-7-sqrt%2813%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which are reciprocal to each other\r<BR>\n" );
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document.write( "and, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=2%29+ ALIGN=MIDDLE  ALT=\"highlight%28p=2%29+\"   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=%28p%5E2%2B2%29x%5E2%2B7x%2B3p=0 ALIGN=MIDDLE  ALT=\"%28p%5E2%2B2%29x%5E2%2B7x%2B3p=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E2%2B2%29x%5E2%2B7x%2B3%2A2=0 ALIGN=MIDDLE  ALT=\"%282%5E2%2B2%29x%5E2%2B7x%2B3%2A2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B7x%2B6=0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B7x%2B6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "roots are: => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%281%2F12%29%2Ai+%28sqrt%2895%29-7i%29 ALIGN=MIDDLE  ALT=\"x=-%281%2F12%29%2Ai+%28sqrt%2895%29-7i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28%281%2F12%29%2Ai+%28sqrt%2895%29%2B7i%29%29+ ALIGN=MIDDLE  ALT=\"x=%28%281%2F12%29%2Ai+%28sqrt%2895%29%2B7i%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and they are reciprocal to each other\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );