document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=7705>Question 7705</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find a polynomial fuction of the smallest possible degree that will satisfy the following conditions:\r<BR>\n" );
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document.write( "f(1)=f(3)=f(6)=0 ; f(4)=-12\r<BR>\n" );
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document.write( "ty </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4252 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=4252\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have 3 roots, at x=1, x=3 and x=6, so we are taking about a cubic, where (x-1)(x-3)(x-6) = 0. The following graph shows just 3 of the possible curves:\r<BR>\n" );
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document.write( "the issue is now to find that ONE curve that passes through (4, -12). All the possible curves are just \"multiples\" of y = (x-1)(x-3)(x-6).\r<BR>\n" );
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document.write( "So, we have y = a(x-1)(x-3)(x-6), where a is a constant, so now put in the x and y values.\r<BR>\n" );
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document.write( "-12 = a(4-1)(4-3)(4-6)<BR>\n" );
document.write( "-12 = a(3)(1)(-2)<BR>\n" );
document.write( "-12 = -6a<BR>\n" );
document.write( "--> a = 2\r<BR>\n" );
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document.write( "so, our required curve is y = 2(x-1)(x-3)(x-6)\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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