document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62976>Question 62976</A>: <I><SPAN STYLE=\"word-break: break-all;\"> FIND THE POLYNOMIAL f(x) OF DEGREE THREE THAT HAS ZEROES AT 1,2, AND 4 SUCH THAT f(0)=-16. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #43810 by </B><A HREF=/tutors/aboutme.mpl?userid=uma><B>uma(370)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=uma><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=43810\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given that the polynomial has zeroes at 1, 2 and 4.\r<BR>\n" );
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document.write( "So the required polynomial will be :\r<BR>\n" );
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document.write( "a(x-1)(x-2)(x-4)\r<BR>\n" );
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document.write( "==> a(x-1)(x^2 - 2x - 4x + 8)\r<BR>\n" );
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document.write( "= a(x-1)(x^2 - 6x + 8)\r<BR>\n" );
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document.write( "= ax^3 - 6ax^2 + 8ax - ax^2 + 6ax - 8a\r<BR>\n" );
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document.write( "= ax^3 - 7ax^2 + 14ax - 8a\r<BR>\n" );
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document.write( "f(0) = - 8a\r<BR>\n" );
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document.write( "==> - 8a =  - 16<BR>\n" );
document.write( "==> a = 2\r<BR>\n" );
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document.write( "Thus f(x) = 2x^3 - 14x^2 + 28x - 16<BR>\n" );
document.write( " is the required polynomial.\r<BR>\n" );
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document.write( "Good Luck!!!\r<BR>\n" );
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document.write( " </SPAN>\n" );
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