document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997519>Question 997519</A>: <I><SPAN STYLE=\"word-break: break-all;\"> form a quadratic equation in x whose roots are the squares of the roots of 2x^2-8x&#65291;1&#65309;0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615565 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=615565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "a quadratic equation in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > whose roots are the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=squares ALIGN=MIDDLE  ALT=\"squares\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the roots of <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-8x%2B1=0 ALIGN=MIDDLE  ALT=\"2x%5E2-8x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find the roots of\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-8x%2B1=0 ALIGN=MIDDLE  ALT=\"2x%5E2-8x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >............use quadratic formula\r<BR>\n" );
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document.write( "<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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%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=x+=+%288+%2B-+sqrt%2864-8+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%288+%2B-+sqrt%2864-8+%29%29%2F4+\"   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+=+%288+%2B-+sqrt%2856+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%288+%2B-+sqrt%2856+%29%29%2F4+\"   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+=+%288+%2B-+sqrt%284%2A14+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%288+%2B-+sqrt%284%2A14+%29%29%2F4+\"   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+=+%28cross%288%294+%2B-+cross%282%29sqrt%2814+%29%29%2Fcross%284%292+ ALIGN=MIDDLE  ALT=\"x+=+%28cross%288%294+%2B-+cross%282%29sqrt%2814+%29%29%2Fcross%284%292+\"   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+=+%284+%2B-+sqrt%2814+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+sqrt%2814+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, exact roots are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284+%2B+sqrt%2814+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%284+%2B+sqrt%2814+%29%29%2F2+\"   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+=+%284+-+sqrt%2814+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%284+-+sqrt%2814+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "approximate:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%284+%2B+3.741657386773941%29%2F2+=7.741657386773941%2F2=3.87 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%284+%2B+3.741657386773941%29%2F2+=7.741657386773941%2F2=3.87\"   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+=+%284+-+3.741657386773941%29%2F2=+0.2583426132260586%2F2=0.13 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%284+-+3.741657386773941%29%2F2=+0.2583426132260586%2F2=0.13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now find their squares:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%5E2+=+14.98 ALIGN=MIDDLE  ALT=\"x%5B1%5D%5E2+=+14.98\"   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%5E2+=0.0169 ALIGN=MIDDLE  ALT=\"x%5B2%5D%5E2+=0.0169\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now use zero product formula to find your equation:\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;\" >\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-14.98%29%28x-0.0169%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-14.98%29%28x-0.0169%29\"   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=x%5E2-0.0169x-14.98x-14.98%2A%28-0.0169%29 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2-0.0169x-14.98x-14.98%2A%28-0.0169%29\"   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=x%5E2-14.9969x%2B0.253162 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2-14.9969x%2B0.253162\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );