document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1036614>Question 1036614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, How would I sketch the graph of a polynomial function that has these indicated number and types of zeros? \r<BR>\n" );
document.write( "\n" );
document.write( "a. 3 real, 2 imaginary <BR>\n" );
document.write( "b. 4 real <BR>\n" );
document.write( "c. 2 imaginary </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #651379 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=651379\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The imaginary are conjugate.  use (x-i) and (x+i). Their product is x^2+1<BR>\n" );
document.write( "Three real could be 1,0 and -1, factors are x,(x-1)(x+1) or x(x^2-1)or x^3-x.  Multiplying that by x^2+1 to get<BR>\n" );
document.write( "x^5+x^3-x^2-x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E5%2Bx%5E3-x%5E2-x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E5%2Bx%5E3-x%5E2-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );