document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=921337>Question 921337</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the quadratic equation if the difference of the squares of the roots is 95 and their difference is 5.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558939 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=558939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  \r<BR>\n" );
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document.write( "let the roots be: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " the difference of the squares of the roots is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=95 ALIGN=MIDDLE  ALT=\"95\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B1%5D%29%5E2+-%28+x%5B2%5D%29%5E2=95 ALIGN=MIDDLE  ALT=\"%28x%5B1%5D%29%5E2+-%28+x%5B2%5D%29%5E2=95\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............eq.1\r<BR>\n" );
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document.write( "their difference is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+ ALIGN=MIDDLE  ALT=\"5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+-+x%5B2%5D=5 ALIGN=MIDDLE  ALT=\"x%5B1%5D+-+x%5B2%5D=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ............eq.2 \r<BR>\n" );
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document.write( "solve the system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B1%5D%29%5E2+-%28+x%5B2%5D%29%5E2=95 ALIGN=MIDDLE  ALT=\"%28x%5B1%5D%29%5E2+-%28+x%5B2%5D%29%5E2=95\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+-+x%5B2%5D=5 ALIGN=MIDDLE  ALT=\"x%5B1%5D+-+x%5B2%5D=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ............eq.2 <BR>\n" );
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document.write( "start with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D-x%5B2%5D=5 ALIGN=MIDDLE  ALT=\"x%5B1%5D-x%5B2%5D=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ............eq.2 ...solve for<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B1%5D+ ALIGN=MIDDLE  ALT=\"+x%5B1%5D+\"   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=x%5B1%5D+=5%2Bx%5B2%5D+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=5%2Bx%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............substitute in eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2Bx%5B2%5D+%29%5E2+-%28+x%5B2%5D%29%5E2=95 ALIGN=MIDDLE  ALT=\"%285%2Bx%5B2%5D+%29%5E2+-%28+x%5B2%5D%29%5E2=95\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............eq.1....solve for<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B2%5D+ ALIGN=MIDDLE  ALT=\"+x%5B2%5D+\"   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=25%2B10x%5B2%5D+%2Bx%5B2%5D+%5E2+-%28+x%5B2%5D%29%5E2=95 ALIGN=MIDDLE  ALT=\"25%2B10x%5B2%5D+%2Bx%5B2%5D+%5E2+-%28+x%5B2%5D%29%5E2=95\"   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=25%2B10x%5B2%5D+%2Bcross%28x%5B2%5D+%5E2%29+-cross%28%28+x%5B2%5D%29%5E2%29=95 ALIGN=MIDDLE  ALT=\"25%2B10x%5B2%5D+%2Bcross%28x%5B2%5D+%5E2%29+-cross%28%28+x%5B2%5D%29%5E2%29=95\"   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=10x%5B2%5D+=95-25 ALIGN=MIDDLE  ALT=\"10x%5B2%5D+=95-25\"   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=10x%5B2%5D+=70 ALIGN=MIDDLE  ALT=\"10x%5B2%5D+=70\"   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=x%5B2%5D+=70%2F10 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=70%2F10\"   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%28x%5B2%5D+=7%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5B2%5D+=7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "go to<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B1%5D+=5%2Bx%5B2%5D+ ALIGN=MIDDLE  ALT=\"+x%5B1%5D+=5%2Bx%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=7 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=7\"   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=x%5B1%5D+=5%2B7 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=5%2B7\"   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%28x%5B1%5D+=12%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5B1%5D+=12%29\"   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=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use zero product rule\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...........plug in<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B1%5D+=12 ALIGN=MIDDLE  ALT=\"+x%5B1%5D+=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=7 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=7\"   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=f%28x%29=%28x-12%29%28x-7%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-12%29%28x-7%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=f%28x%29=x%5E2-7x-12x%2B7%2A12 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2-7x-12x%2B7%2A12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f%28x%29=x%5E2-19x%2B84%29 ALIGN=MIDDLE  ALT=\"highlight%28f%28x%29=x%5E2-19x%2B84%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-15%2C+25%2C+-10%2C+100%2C+x%5E2-19x%2B84%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-15%2C+25%2C+-10%2C+100%2C+x%5E2-19x%2B84%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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