document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128657>Question 128657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ok this one I really do not understand becuase they do not give me a value for x or anything.\r<BR>\n" );
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document.write( "Part A) Calculate the value of the discriminant of x^2+x+3=0\r<BR>\n" );
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document.write( "Part B) by examining teh sign of the discriminant in part a, how many x-intercepts would the graph of y = x^2+x+3 have? Why?\r<BR>\n" );
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document.write( "I know that to get the discrimant the equation is b^2 - 4ac, and that if the discriminant is positive the the solutions will be real numbers, and if it is a negative you will have two complex solutions.  but how do I solve this if I do not know what the value of b is or the value of A and C </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94123 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=94123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  From the 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( "the discriminant consists of all of the terms in the square root. So the discriminant is\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;\" >\r<BR>\n" );
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document.write( "the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic.\r<BR>\n" );
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document.write( "Now let's find the discriminant for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2Bx%2B3 ALIGN=MIDDLE  ALT=\"y=x%5E2%2Bx%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=3 ALIGN=MIDDLE  ALT=\"c=3\"   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 given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=%281%29%5E2-4%2A1%2A3 ALIGN=MIDDLE  ALT=\"D=%281%29%5E2-4%2A1%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=1, c=3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=1-4%2A1%2A3 ALIGN=MIDDLE  ALT=\"D=1-4%2A1%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 1 to get 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=1-12 ALIGN=MIDDLE  ALT=\"D=1-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -4*1*3 to get -12\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=-11 ALIGN=MIDDLE  ALT=\"D=-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine 1 and -12 to get -11\r<BR>\n" );
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document.write( "Since the discriminant equals -11  (which is less than zero) , this means  there are two complex solutions.\r<BR>\n" );
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document.write( "Notice if we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2Bx%2B3 ALIGN=MIDDLE  ALT=\"y=x%5E2%2Bx%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2Bx%2B3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2Bx%2B3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and we can see that there are two complex solutions. So this visually verifies our answer.\r<BR>\n" );
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