document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133011>Question 133011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi.<BR>\n" );
document.write( "Please help. I am lost-my mind is swimming with all the steps and I got lost twice-I need HELP!<BR>\n" );
document.write( "The problem is: State the value of the discriminant and the number of real solutions. t^2+14t+49=0<BR>\n" );
document.write( "Thank You. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97220 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=97220\">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=t%5E2%2B14t%2B49 ALIGN=MIDDLE  ALT=\"y=t%5E2%2B14t%2B49\"   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=%2814%29%5E2-4%2A1%2A49 ALIGN=MIDDLE  ALT=\"D=%2814%29%5E2-4%2A1%2A49\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=14, c=49\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=196-4%2A1%2A49 ALIGN=MIDDLE  ALT=\"D=196-4%2A1%2A49\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 14 to get 196\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=196-196 ALIGN=MIDDLE  ALT=\"D=196-196\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -4*1*49 to get -196\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=0 ALIGN=MIDDLE  ALT=\"D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine 196 and -196 to get 0\r<BR>\n" );
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document.write( "Since the discriminant equals 0 , this means  there is one real solution. Remember if the discriminant is equal to zero, then the quadratic will have one real solution.\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=t%5E2%2B14t%2B49 ALIGN=MIDDLE  ALT=\"y=t%5E2%2B14t%2B49\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can see that there is one real solution. So this verifies our answer.\r<BR>\n" );
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