document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198236>Question 198236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you tell me please if these are correct.<BR>\n" );
document.write( "1. root12((-10))^12<BR>\n" );
document.write( "Answer N not a real number<BR>\n" );
document.write( "2. Use the foil method to find the product<BR>\n" );
document.write( "(9x^8-7)(x^9-5)=<BR>\n" );
document.write( "Answer 9x^17-7x9-45x^8+35<BR>\n" );
document.write( "3. For the following equation state the value of the disctiminant and then describle the nature of the solution<BR>\n" );
document.write( "12x^2-8x+7=0<BR>\n" );
document.write( "Answer -272<BR>\n" );
document.write( "4. Factor<BR>\n" );
document.write( "a^2+6a+9=<BR>\n" );
document.write( "Answer (a+3)^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148685 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=148685\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "Is the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%2812%2C%28-10%29%5E12%29 ALIGN=MIDDLE  ALT=\"root%2812%2C%28-10%29%5E12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >??? If so, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%2812%2C%28-10%29%5E12%29=10 ALIGN=MIDDLE  ALT=\"root%2812%2C%28-10%29%5E12%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "On the other hand, if the expression is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28root%2812%2C-10%29%29%5E12 ALIGN=MIDDLE  ALT=\"%28root%2812%2C-10%29%29%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then result is NOT a real number. Why? You CANNOT take an even root of a negative number and get a real number (eg you can't take the square root of -2).\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "You are correct. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x%5E8-7%29%2A%28x%5E9-5%29=9x%5E17-7x%5E9-45x%5E8%2B35 ALIGN=MIDDLE  ALT=\"%289x%5E8-7%29%2A%28x%5E9-5%29=9x%5E17-7x%5E9-45x%5E8%2B35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "# 3\r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2-8x%2B7 ALIGN=MIDDLE  ALT=\"12x%5E2-8x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=12 ALIGN=MIDDLE  ALT=\"a=12\"   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=7 ALIGN=MIDDLE  ALT=\"c=7\"   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=D=b%5E2-4ac ALIGN=MIDDLE  ALT=\"D=b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the discriminant formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=%28-8%29%5E2-4%2812%29%287%29 ALIGN=MIDDLE  ALT=\"D=%28-8%29%5E2-4%2812%29%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=12 ALIGN=MIDDLE  ALT=\"a=12\"   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=7 ALIGN=MIDDLE  ALT=\"c=7\"   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=D=64-4%2812%29%287%29 ALIGN=MIDDLE  ALT=\"D=64-4%2812%29%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   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=D=64-336 ALIGN=MIDDLE  ALT=\"D=64-336\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2812%29%287%29 ALIGN=MIDDLE  ALT=\"4%2812%29%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2848%29%287%29=336 ALIGN=MIDDLE  ALT=\"%2848%29%287%29=336\"   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=D=-272 ALIGN=MIDDLE  ALT=\"D=-272\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=336 ALIGN=MIDDLE  ALT=\"336\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-272 ALIGN=MIDDLE  ALT=\"-272\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the discriminant is less than zero, this means that there are two complex solutions.\r<BR>\n" );
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document.write( "In other words, there are no real solutions.\r<BR>\n" );
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document.write( "You got the right discriminant value, but you forgot to mention what that meant in terms of the number of solutions.\r<BR>\n" );
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document.write( "# 4\r<BR>\n" );
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document.write( "You are correct, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B6a%2B9 ALIGN=MIDDLE  ALT=\"a%5E2%2B6a%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"%28a%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You can verify the answer by \r<BR>\n" );
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document.write( "a) Graphing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B6a%2B9 ALIGN=MIDDLE  ALT=\"a%5E2%2B6a%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"%28a%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the same grid. You'll see that they are the same graph, or...\r<BR>\n" );
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document.write( "b) You can FOIL <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"%28a%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B6a%2B9 ALIGN=MIDDLE  ALT=\"a%5E2%2B6a%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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