document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1041375>Question 1041375</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the roots of the quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+x+%2B6+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+x+%2B6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta ALIGN=MIDDLE  ALT=\"beta\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find the quadratic equation whose roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha+%2B+1%2F%282%2Abeta%29 ALIGN=MIDDLE  ALT=\"alpha+%2B+1%2F%282%2Abeta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta+%2B+1%2F%282%2Aalpha%29 ALIGN=MIDDLE  ALT=\"beta+%2B+1%2F%282%2Aalpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #656408 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=656408\">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=2x%5E2+%2B+x+%2B6+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+x+%2B6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+x%2F2+%2B3+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x%2F2+%2B3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha%2Bbeta+=+-1%2F2 ALIGN=MIDDLE  ALT=\"alpha%2Bbeta+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha%2Abeta+=+3 ALIGN=MIDDLE  ALT=\"alpha%2Abeta+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For the new quadratic equation:\r<BR>\n" );
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document.write( "The coefficient of x = -(Sum of the roots)\r<BR>\n" );
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document.write( "= -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28alpha+%2B+1%2F%282%2Abeta%29+%2B+beta+%2B+1%2F%282%2Aalpha%29%29 ALIGN=MIDDLE  ALT=\"%28alpha+%2B+1%2F%282%2Abeta%29+%2B+beta+%2B+1%2F%282%2Aalpha%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=%28alpha++%2B+beta+%2B+1%2F%282%2Abeta%29%2B+1%2F%282%2Aalpha%29%29+=+-%28alpha++%2B+beta+%2B+%0D%0A%281%2F2%29%2A%28%28alpha%2Bbeta%29%2F%28alpha%2Abeta%29%29%29 ALIGN=MIDDLE   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=%28+-1%2F2+%2B%281%2F2%29%2A%28%28-1%2F2%29%2F3%29%29 ALIGN=MIDDLE  ALT=\"%28+-1%2F2+%2B%281%2F2%29%2A%28%28-1%2F2%29%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7/12\r<BR>\n" );
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document.write( "The constant in the quadratic equation = product of roots\r<BR>\n" );
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document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28alpha+%2B+1%2F%282%2Abeta%29%29%28beta+%2B+1%2F%282%2Aalpha%29%29%29 ALIGN=MIDDLE  ALT=\"%28alpha+%2B+1%2F%282%2Abeta%29%29%28beta+%2B+1%2F%282%2Aalpha%29%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=alpha%2Abeta+%2B1+%2B+1%2F%284%2Aalpha%2Abeta%29+=+3%2B1%2B1%2F12+=+49%2F12 ALIGN=MIDDLE  ALT=\"alpha%2Abeta+%2B1+%2B+1%2F%284%2Aalpha%2Abeta%29+=+3%2B1%2B1%2F12+=+49%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "===> the quadratic equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B+%287%2F12%29x+%2B+49%2F12+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B+%287%2F12%29x+%2B+49%2F12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or after clearing fractions,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2+%2B+7x+%2B+49+=+0 ALIGN=MIDDLE  ALT=\"12x%5E2+%2B+7x+%2B+49+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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