document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187810>Question 187810</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3. Use the two roots given by the quadratic equation<BR>\n" );
document.write( "a. find a formula for the sum of the roots<BR>\n" );
document.write( "b. find a formula for the product of the roots<BR>\n" );
document.write( "c. without solving tell the sum and product of the solutions of 2x^2+5x-3=0\r<BR>\n" );
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document.write( "I don't even understand the question at all....I feel like it doesn't make sense </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140811 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=140811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember, the quadratic formula is \r<BR>\n" );
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document.write( "which really breaks down to \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-b+%2B+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-b+%2B+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-b+-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-b+-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%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=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;\" > are the two roots\r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "find a formula for the 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=x%5B1%5D%2Bx%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D%2Bx%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the roots <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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b+%2B+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29%2B%28-b+-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-b+%2B+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29%2B%28-b+-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the formulas from above.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b+%2B+sqrt%28+b%5E2-4ac+%29+-+b+-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-b+%2B+sqrt%28+b%5E2-4ac+%29+-+b+-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2b%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-2b%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2Fa ALIGN=MIDDLE  ALT=\"-b%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the sum of the roots <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;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2Fa ALIGN=MIDDLE  ALT=\"-b%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%2Bx%5B2%5D=-b%2Fa ALIGN=MIDDLE  ALT=\"x%5B1%5D%2Bx%5B2%5D=-b%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b) \r<BR>\n" );
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document.write( "find a formula for the product of the roots\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%2Ax%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D%2Ax%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the two roots.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-b+%2B+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29%29%28%28-b+-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the formulas above\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-b+%2B+sqrt%28+b%5E2-4ac+%29%29%28-b+-+sqrt%28+b%5E2-4ac+%29%29%29%2F%28%282a%29%282a%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-b%29%5E2+%2B+%28sqrt%28+b%5E2-4ac+%29%29%5E2%29%2F%28%282a%29%282a%29%29 ALIGN=MIDDLE  ALT=\"%28%28-b%29%5E2+%2B+%28sqrt%28+b%5E2-4ac+%29%29%5E2%29%2F%28%282a%29%282a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL by using the difference of squares formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%5E2-%28b%5E2-4ac%29%29%2F%284a%5E2%29 ALIGN=MIDDLE  ALT=\"%28b%5E2-%28b%5E2-4ac%29%29%2F%284a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square each term.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%5E2-b%5E2%2B4ac%29%2F%284a%5E2%29 ALIGN=MIDDLE  ALT=\"%28b%5E2-b%5E2%2B4ac%29%2F%284a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284ac%29%2F%284a%5E2%29 ALIGN=MIDDLE  ALT=\"%284ac%29%2F%284a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Fa ALIGN=MIDDLE  ALT=\"c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the formula for the product of the roots <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;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Fa ALIGN=MIDDLE  ALT=\"c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%2Ax%5B2%5D=c%2Fa ALIGN=MIDDLE  ALT=\"x%5B1%5D%2Ax%5B2%5D=c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c)\r<BR>\n" );
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document.write( "without solving tell the sum and product of the solutions of 2x^2+5x-3=0\r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B5x-3=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B5x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5 ALIGN=MIDDLE  ALT=\"b=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-3 ALIGN=MIDDLE  ALT=\"c=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Sum of the roots: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%2Bx%5B2%5D=-b%2Fa=-5%2F2 ALIGN=MIDDLE  ALT=\"x%5B1%5D%2Bx%5B2%5D=-b%2Fa=-5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Product of the roots: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%2Ax%5B2%5D=-3%2F2 ALIGN=MIDDLE  ALT=\"x%5B1%5D%2Ax%5B2%5D=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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