document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083875>Question 1083875</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A monic quadratic is a quadratic in which the coefficient <BR>\n" );
document.write( "of the quadratic term is 1. For example, r^2 - 3r + 7 <BR>\n" );
document.write( "is a monic quadratic, but 3t^2 - 3t + 1 is not.\r<BR>\n" );
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document.write( "A teacher writes a monic quadratic on the board.\r<BR>\n" );
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document.write( "Joanie copies the quadratic onto her paper, but writes <BR>\n" );
document.write( "down the wrong constant term (but the correct quadratic <BR>\n" );
document.write( "and linear terms).<BR>\n" );
document.write( "She correctly factors the quadratic that she wrote down on<BR>\n" );
document.write( "her paper, and determines that her quadratic has roots -16 and 2.\r<BR>\n" );
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document.write( "Kelvin copies the quadratic onto his paper, but he writes down <BR>\n" );
document.write( "the wrong coefficient for the linear term (but the correct <BR>\n" );
document.write( "quadratic and constant terms). \r<BR>\n" );
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document.write( "He correctly factors the quadratic that he wrote down, and <BR>\n" );
document.write( "determines that his quadratic has roots -36 and 2.\r<BR>\n" );
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document.write( "What are the roots of the quadratic that the teacher wrote <BR>\n" );
document.write( "on the board? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697931 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20054)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=697931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A monic quadratic is a quadratic in which the coefficient <BR>\n" );
document.write( "of the quadratic term is 1. For example, $r^2 - 3r + 7$ <BR>\n" );
document.write( "is a monic quadratic, but $3t^2 - 3t + 1$ is not.\r<BR>\n" );
document.write( "\n" );
document.write( "A teacher writes a monic quadratic on the board.<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "The teacher wrote this:  x² + Ax + B\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "Joanie copies the quadratic onto her paper, but writes <BR>\n" );
document.write( "down the wrong constant term (but the correct quadratic <BR>\n" );
document.write( "and linear terms). <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Joanie copied this:      x² + Ax + C\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "She correctly factors the quadratic that she wrote down on <BR>\n" );
document.write( "her paper, and determines that her quadratic has roots -16 and 2.<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "So Joanie got this:                  x=-16; x=2\r\n" );
document.write( "So Joanie had this before:          x+16=0; x-2=0 \r\n" );
document.write( "So Joanie had this factorization:    (x+16)(x-2)\r\n" );
document.write( "So Joanie copied:                    x²+14x-32  \r\n" );
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document.write( "Since Joanie had the right linear term, A = 14,\r\n" );
document.write( "so the teacher wrote this:  x² + 14x + B \r\n" );
document.write( "</PRE><BR>\n" );
document.write( "Kelvin copies the quadratic onto his paper, but he writes down <BR>\n" );
document.write( "the wrong coefficient for the linear term (but the correct <BR>\n" );
document.write( "quadratic and constant terms).<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Kevin copied this:   x² + Dx + B  \r\n" );
document.write( "</PRE><BR>\n" );
document.write( "He correctly factors the quadratic that he wrote down, and <BR>\n" );
document.write( "determines that his quadratic has roots -36 and 2.<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "So Kevin got this:                  x=-36; x=2\r\n" );
document.write( "So Kevin had this before:           x+36=0, x-2=0 \r\n" );
document.write( "So Kevin had this factorization:    (x+36)(x-2)\r\n" );
document.write( "So Kevin copied:                    x²+34x-72  \r\n" );
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document.write( "Since Kevin had the right constant term, B = -72\r\n" );
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document.write( "So the teacher wrote this:  x² + 14x - 72 \r\n" );
document.write( "</PRE><BR>\n" );
document.write( "What are the roots of the quadratic that the teacher wrote <BR>\n" );
document.write( "on the board?<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "I'll leave that last part up to you!!!  Factor, set = 0, and \r\n" );
document.write( "solve for the values of x, which are the roots. \r\n" );
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document.write( "Edwin</PRE></b> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );