document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=839474>Question 839474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that the quadratic equation x^2-3x+1=0 has 2 different roots, create a quadratic equation, so that each of its roots will be 1 more than the corresponding root of the given quadratic equation.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #505716 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=505716\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first thing we need to do is find the roots of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B1=0 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You will notice that this polynomial will not factor evenly, so we will have to find the roots by using the quadratic formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Doing this will give us our two roots:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%2Bsqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"%28%283%2Bsqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283-sqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"%28%283-sqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To find a new quadratic equation with roots that are one more than each of the roots of our original equation, we need to add 1 to each of the original roots:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%2Bsqrt%285%29%29%2F2%29%2B1 ALIGN=MIDDLE  ALT=\"%28%283%2Bsqrt%285%29%29%2F2%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%285%2Bsqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"%28%285%2Bsqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283-sqrt%285%29%29%2F2%29%2B1 ALIGN=MIDDLE  ALT=\"%28%283-sqrt%285%29%29%2F2%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%285-sqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"%28%285-sqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next, we will put these roots into factored form:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%28%285%2Bsqrt%285%29%29%2F2%29%29%2A%28x-%28%285-sqrt%285%29%29%2F2%29%29 ALIGN=MIDDLE  ALT=\"%28x-%28%285%2Bsqrt%285%29%29%2F2%29%29%2A%28x-%28%285-sqrt%285%29%29%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Finally, we need to expand our factors by multiplying via the FOIL method, which will give us our final answer:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x%2B5=0 ALIGN=MIDDLE  ALT=\"x%5E2-5x%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );