document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285939>Question 285939</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation with roots that are the negative reciprocals of the roots of ax^2 +bx +c =0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207356 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=207356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28b%2Fa%29%2Ax+%2B+%28c%2Fa%29+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28b%2Fa%29%2Ax+%2B+%28c%2Fa%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If the roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D ALIGN=MIDDLE  ALT=\"r%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D ALIGN=MIDDLE  ALT=\"r%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+r%5B1%5D%29%2A%28x+-+r%5B2%5D%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+r%5B1%5D%29%2A%28x+-+r%5B2%5D%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+%28r%5B1%5D+%2B+r%5B2%5D%29%2Ax+%2B+r%5B1%5D%2Ar%5B2%5D+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+%28r%5B1%5D+%2B+r%5B2%5D%29%2Ax+%2B+r%5B1%5D%2Ar%5B2%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Comparing the equations:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28r%5B1%5D+%2B+r%5B2%5D%29+=+b%2Fa ALIGN=MIDDLE  ALT=\"-%28r%5B1%5D+%2B+r%5B2%5D%29+=+b%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D%2Ar%5B2%5D+=+c%2Fa ALIGN=MIDDLE  ALT=\"r%5B1%5D%2Ar%5B2%5D+=+c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll say<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B01%5D+=+-%281%2Fr%5B1%5D%29 ALIGN=MIDDLE  ALT=\"r%5B01%5D+=+-%281%2Fr%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B02%5D+=+-%281%2Fr%5B2%5D%29 ALIGN=MIDDLE  ALT=\"r%5B02%5D+=+-%281%2Fr%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D+=+-%281%2Fr%5B01%5D%29 ALIGN=MIDDLE  ALT=\"r%5B1%5D+=+-%281%2Fr%5B01%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D+=+-%281%2Fr%5B02%5D%29 ALIGN=MIDDLE  ALT=\"r%5B2%5D+=+-%281%2Fr%5B02%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "from (2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2Fr%5B01%5D%29%2A%28-1%2Fr%5B02%5D%29+=+c%2Fa ALIGN=MIDDLE  ALT=\"%28-1%2Fr%5B01%5D%29%2A%28-1%2Fr%5B02%5D%29+=+c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28r%5B01%5D%2Ar%5B02%5D%29+=+c%2Fa ALIGN=MIDDLE  ALT=\"1%2F%28r%5B01%5D%2Ar%5B02%5D%29+=+c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B01%5D%2Ar%5B02%5D+=+a%2Fc ALIGN=MIDDLE  ALT=\"r%5B01%5D%2Ar%5B02%5D+=+a%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "from (1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28-1%2Fr%5B01%5D+-+1%2Fr%5B02%5D%29+=+b%2Fa ALIGN=MIDDLE  ALT=\"-%28-1%2Fr%5B01%5D+-+1%2Fr%5B02%5D%29+=+b%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fr%5B01%5D+%2B+1%2Fr%5B02%5D+=+b%2Fa ALIGN=MIDDLE  ALT=\"1%2Fr%5B01%5D+%2B+1%2Fr%5B02%5D+=+b%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B01%5D%2Ar%5B02%5D ALIGN=MIDDLE  ALT=\"r%5B01%5D%2Ar%5B02%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B02%5D+%2B+r%5B01%5D+=+%28b%2Fa%29%2Ar%5B01%5D%2Ar%5B02%5D ALIGN=MIDDLE  ALT=\"r%5B02%5D+%2B+r%5B01%5D+=+%28b%2Fa%29%2Ar%5B01%5D%2Ar%5B02%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B02%5D+%2B+r%5B01%5D+=+%28b%2Fa%29%2A%28a%2Fc%29 ALIGN=MIDDLE  ALT=\"r%5B02%5D+%2B+r%5B01%5D+=+%28b%2Fa%29%2A%28a%2Fc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B01%5D+%2B+r%5B02%5D+=+b%2Fc ALIGN=MIDDLE  ALT=\"r%5B01%5D+%2B+r%5B02%5D+=+b%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+%28r%5B01%5D+%2B+r%5B02%5D%29%2Ax+%2B+r%5B01%5D%2Ar%5B02%5D+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+%28r%5B01%5D+%2B+r%5B02%5D%29%2Ax+%2B+r%5B01%5D%2Ar%5B02%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+%28b%2Fc%29%2Ax+%2B+a%2Fc+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+%28b%2Fc%29%2Ax+%2B+a%2Fc+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cx%5E2+-+bx+%2B+a+=+0 ALIGN=MIDDLE  ALT=\"cx%5E2+-+bx+%2B+a+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There could be a flaw somewhere -look it over\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );