document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=896799>Question 896799</A>: <I><SPAN STYLE=\"word-break: break-all;\"> compute value of discriminant and give the number of real solutions of this quadratic equation.<BR>\n" );
document.write( "2x^2-2x+1=0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #543751 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=543751\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic_formula.solver>Quadratic Formula</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Let's use the quadratic formula to solve for x:<BR><BR>\n" );
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document.write( "  Starting with the general quadratic<BR>\n" );
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document.write( "  the general solution using the quadratic equation is:<BR>\n" );
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document.write( "  So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2-2%2Ax%2B1=0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2-2%2Ax%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <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=-2 ALIGN=MIDDLE  ALT=\"b=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=1 ALIGN=MIDDLE  ALT=\"c=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=2, b=-2, and c=1<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -2 to get 2<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+sqrt%28+4-4%2A2%2A1+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%28+4-4%2A2%2A1+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -2 to get 4  (note: remember when you square -2, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%5E2=-2%2A-2=4 ALIGN=MIDDLE  ALT=\"%28-2%29%5E2=-2%2A-2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+sqrt%28+4%2B-8+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%28+4%2B-8+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A1%2A2 ALIGN=MIDDLE  ALT=\"-4%2A1%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+sqrt%28+-4+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%28+-4+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+2%2Ai%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+2%2Ai%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+2%2Ai%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+2%2Ai%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 2 to get 4<BR>\n" );
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document.write( "  After simplifying, the quadratic has roots of<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2%2B1%2F2%2Ai ALIGN=MIDDLE  ALT=\"x=1%2F2%2B1%2F2%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2-1%2F2%2Ai ALIGN=MIDDLE  ALT=\"x=1%2F2-1%2F2%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The discriminant is -4 and so there are no real solutions </SPAN>\n" );
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