document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=839475>Question 839475</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that the quadratic equation x^2-2x-5=0 has 2 different roots, and a second quadratic equation has 2 roots, each of which 2 less than the corresponding root of the given quadratic equation. If the second quadratic equation is x^2+ax+b=0, find the value of a and b. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #505737 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=505737\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given that the quadratic equation x^2-2x-5=0 has 2 different roots, and a second quadratic equation has 2 roots, each of which 2 less than the corresponding root of the given quadratic equation. If the second quadratic equation is x^2+ax+b=0, find the value of a and b.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-5=0 ALIGN=MIDDLE  ALT=\"x%5E2-2x-5=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=x%5E2-2x%2B1-1-5=0 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B1-1-5=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=%28x-1%29%5E2-6=0 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2-6=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=%28x-1%29%5E2=6 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(x-1) = +/- sqrt(6)\r<BR>\n" );
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document.write( "The roots of the second equation will be \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%29-2 ALIGN=MIDDLE  ALT=\"sqrt%286%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%286%29-2 ALIGN=MIDDLE  ALT=\"-sqrt%286%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "sum  of roots = -4\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=sqrt%286%29-2 ALIGN=MIDDLE  ALT=\"sqrt%286%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%286%29-2 ALIGN=MIDDLE  ALT=\"-sqrt%286%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=-2\r<BR>\n" );
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document.write( "The general equation is<BR>\n" );
document.write( "x^2-sum of roots(x)+product of the roots=0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%28-4%29x%2B%28-2%29=0 ALIGN=MIDDLE  ALT=\"x%5E2-%28-4%29x%2B%28-2%29=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=x%5E2%2B4x-2=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "comparing the equation with\r<BR>\n" );
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document.write( "x^2+ax+b=0\r<BR>\n" );
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document.write( "we get<BR>\n" );
document.write( "a=4, b=-2 </SPAN>\n" );
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