document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029945>Question 1029945</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial function f(x) of degree 3 with real coefficients that satisfies the given conditions.<BR>\n" );
document.write( " <BR>\n" );
document.write( "zero of 2 and zero of 4 having multiplicity 2; f(1)=-18 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644859 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=644859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+k%28x-2%29%28x-4%29%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+k%28x-2%29%28x-4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some undetermined constant k.\r<BR>\n" );
document.write( "\n" );
document.write( "Now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29+=+k%281-2%29%281-4%29%5E2+=+-18 ALIGN=MIDDLE  ALT=\"f%281%29+=+k%281-2%29%281-4%29%5E2+=+-18\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> -9k = -18 ==> k = 2.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%28x-2%29%28x-4%29%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%28x-2%29%28x-4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the polynomial function of degree 3.  (Just do the necessary expansion.) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );