document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=21998>Question 21998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It would be nice if someone could show me how to solve this problem.<BR>\n" );
document.write( "Thanks in advance.\r<BR>\n" );
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document.write( "Find a polynomial equation that has the zeros x= +1,-1 and x= +2,-2 and passes through the point (3,5). Some blanks may contain zeros.\r<BR>\n" );
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document.write( "f(x)=(___)X­^4+(____)X^3-(____)X^2+(____)X+(____) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #11815 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=11815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Zeroes at +-1 implies a factor of (x^2-1)<BR>\n" );
document.write( " Zeroes at +-2 implies a factor of (x^2-4)<BR>\n" );
document.write( " EQUATION:<BR>\n" );
document.write( " y = k(x^2-1)(x^2-4)<BR>\n" );
document.write( "We need to find \"k\".<BR>\n" );
document.write( "We have a point: when x=3, y=5.<BR>\n" );
document.write( "Substitute that values in to get:<BR>\n" );
document.write( " 5 = k(9-1)(9-4)<BR>\n" );
document.write( " 5 = k(8)(5)<BR>\n" );
document.write( " k = 1/8<BR>\n" );
document.write( "The equation you want is y = (1/8)(x^2-1)(x^2-4)<BR>\n" );
document.write( "Multiply that out to get <BR>\n" );
document.write( "y = (1/8)[x^4-5x^2+4]<BR>\n" );
document.write( "y = (1/8)x^4 = (5/8)x^2 +(1/2)\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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