document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181964>Question 1181964</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many real number solutions does the equation y=2x^2−8x+8 have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811915 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=811915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How many real number solutions does the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2-8x%2B8 ALIGN=MIDDLE  ALT=\"y=2x%5E2-8x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > have?\r<BR>\n" );
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document.write( "use discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac%3E0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2-8x%2B8 ALIGN=MIDDLE  ALT=\"y=2x%5E2-8x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  will have  two distinct real number solutions \r<BR>\n" );
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document.write( "in your case <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=-8 ALIGN=MIDDLE  ALT=\"b=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=8 ALIGN=MIDDLE  ALT=\"c=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substitute in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac%3E0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac%3E0\"   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=%28-8%29%5E2-4%2A2%2A8%3E0 ALIGN=MIDDLE  ALT=\"%28-8%29%5E2-4%2A2%2A8%3E0\"   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=64-64%3E0 ALIGN=MIDDLE  ALT=\"64-64%3E0\"   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=0%3E0 ALIGN=MIDDLE  ALT=\"0%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> false => the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2%E2%88%928x%2B8 ALIGN=MIDDLE  ALT=\"y=2x%5E2%E2%88%928x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > have no  two distinct real number solutions\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2-8x%2B8 ALIGN=MIDDLE  ALT=\"y=2x%5E2-8x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > will have  a repeated real number solution\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-8%29%5E2-4%2A2%2A8=0 ALIGN=MIDDLE  ALT=\"%28-8%29%5E2-4%2A2%2A8=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=64-64=0 ALIGN=MIDDLE  ALT=\"64-64=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=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ->true=> the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2-8x%2B8 ALIGN=MIDDLE  ALT=\"y=2x%5E2-8x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > will have  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=one ALIGN=MIDDLE  ALT=\"one\"   DISABLED_style= \"max-width:90%; height:auto;\" >a repeated real number solution\r<BR>\n" );
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