document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=466180>Question 466180</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find all of the zeros and state any multiplicity for<BR>\n" );
document.write( "j(x)=-2x^3 + 6x^2 - 9/2x\r<BR>\n" );
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document.write( "k(x)=x^3 - 28x -48\r<BR>\n" );
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document.write( "m(x)= x^4 - x^2 - 20  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #319623 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=319623\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find all of the zeros and state any multiplicity for<BR>\n" );
document.write( "j(x)=-2x^3 + 6x^2 - 9/2x <BR>\n" );
document.write( "k(x)=x^3 - 28x -48 <BR>\n" );
document.write( "m(x)= x^4 - x^2 - 20<BR>\n" );
document.write( "...<BR>\n" );
document.write( "j(x)=-2x^3+6x^2-9/2x=0<BR>\n" );
document.write( "factor out 2x<BR>\n" );
document.write( "2x(x^2+3x+9/4)=0<BR>\n" );
document.write( "2x(x+3/2)^2=0<BR>\n" );
document.write( "2x=0<BR>\n" );
document.write( "x=0<BR>\n" );
document.write( "or<BR>\n" );
document.write( "x=-3/2 (multiplicity 2)<BR>\n" );
document.write( "zeros: 0, -3/2 , -3/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "k(x)=x^3-28x-48=0<BR>\n" );
document.write( "x=-2 (from graphing calculator)<BR>\n" );
document.write( "By long division or synthetic division<BR>\n" );
document.write( "(x^3-28x-48)/(x+2)=x^2-2x-24=(x-6)(x+4)<BR>\n" );
document.write( "zeros: -4, -2, 6<BR>\n" );
document.write( "..<BR>\n" );
document.write( "m(x)= x^4-x^2-20=0<BR>\n" );
document.write( "         (x^2-5)(x^2+4)=0<BR>\n" );
document.write( "x^2-5=0<BR>\n" );
document.write( "x^2=5<BR>\n" );
document.write( "x=±&#8730;5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "x^2+4=0<BR>\n" );
document.write( "x^2=-4<BR>\n" );
document.write( "x=±2 i (2 imaginary roots)<BR>\n" );
document.write( "zeros: -&#8730;5, &#8730;5 and 2 imaginary roots </SPAN>\n" );
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