document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=975001>Question 975001</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a degree 3 polynomial that has zeros -2, 3 and 6 and in which the coefficient of x^2 is -14?\r<BR>\n" );
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document.write( "ok.. I know the zeros would be (x+2) (x-3) (x-6).. then I get lost with the -14x^2..<BR>\n" );
document.write( "can someone please help find what the polynomial is? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #596825 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=596825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Any cubic polynomial with roots -2,3,6 will be of this form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%28x%2B2%29%28x-3%29%28x-6%29 ALIGN=MIDDLE  ALT=\"k%28x%2B2%29%28x-3%29%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where k is some constant\r<BR>\n" );
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document.write( "Let's expand out the polynomial\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%28x%2B2%29%28x-3%29%28x-6%29 ALIGN=MIDDLE  ALT=\"k%28x%2B2%29%28x-3%29%28x-6%29\"   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=k%28x%2B2%29%28x%5E2-9x%2B18%29 ALIGN=MIDDLE  ALT=\"k%28x%2B2%29%28x%5E2-9x%2B18%29\"   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=k%28x%28x%5E2-9x%2B18%29%2B2%28x%5E2-9x%2B18%29%29 ALIGN=MIDDLE  ALT=\"k%28x%28x%5E2-9x%2B18%29%2B2%28x%5E2-9x%2B18%29%29\"   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=k%28x%5E3-9x%5E2%2B18x%2B2x%5E2-18x%2B36%29 ALIGN=MIDDLE  ALT=\"k%28x%5E3-9x%5E2%2B18x%2B2x%5E2-18x%2B36%29\"   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=k%28x%5E3-7x%5E2%2B36%29 ALIGN=MIDDLE  ALT=\"k%28x%5E3-7x%5E2%2B36%29\"   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=k%2Ax%5E3-7kx%5E2%2B36k ALIGN=MIDDLE  ALT=\"k%2Ax%5E3-7kx%5E2%2B36k\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The x^2 term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7kx%5E2 ALIGN=MIDDLE  ALT=\"-7kx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We want the x^2 coefficient to be -14, so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7k=-14 ALIGN=MIDDLE  ALT=\"-7k=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+2 ALIGN=MIDDLE  ALT=\"k+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since k = 2, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2Ax%5E3-7kx%5E2%2B36k ALIGN=MIDDLE  ALT=\"k%2Ax%5E3-7kx%5E2%2B36k\"   DISABLED_style= \"max-width:90%; height:auto;\" > turns into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3-14x%5E2%2B72 ALIGN=MIDDLE  ALT=\"2x%5E3-14x%5E2%2B72\"   DISABLED_style= \"max-width:90%; height:auto;\" > after k is replaced with 2 and you simplify\r<BR>\n" );
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document.write( "------------------------------------------------------------------------------------------------------------------------\r<BR>\n" );
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document.write( "Jim\r<BR>\n" );
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document.write( "------------------------------------------------------------------------------------------------------------------------ </SPAN>\n" );
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