document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=322743>Question 322743</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me figure out how to find the complex zeros of the equation: <BR>\n" );
document.write( "f(x)=4x^3+19x^2-61x+14 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #231018 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=231018\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since there are three roots and complex roots come in pairs, at least one must be real.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+5%2C+-500%2C+500%2C+4x%5E3%2B19x%5E2-61x%2B14%29 ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+5%2C+-500%2C+500%2C+4x%5E3%2B19x%5E2-61x%2B14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "All three roots are real for this equation.<BR>\n" );
document.write( "Looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > are roots. <BR>\n" );
document.write( "Verify using the equation.<BR>\n" );
document.write( "I'll do one, you verify the other.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3%2B19x%5E2-61x%2B14=4%28-7%29%5E3%2B19%2849%29-61%28-7%29%2B14 ALIGN=MIDDLE  ALT=\"4x%5E3%2B19x%5E2-61x%2B14=4%28-7%29%5E3%2B19%2849%29-61%28-7%29%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3%2B19x%5E2-61x%2B14=-1372%2B931%2B427%2B14 ALIGN=MIDDLE  ALT=\"4x%5E3%2B19x%5E2-61x%2B14=-1372%2B931%2B427%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3%2B19x%5E2-61x%2B14=0 ALIGN=MIDDLE  ALT=\"4x%5E3%2B19x%5E2-61x%2B14=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now that you have two factors. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%28x-2%29=x%5E2%2B5x-14 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%28x-2%29=x%5E2%2B5x-14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can use polynomial long division to find the remaining factor.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E3%2B19x%5E2-61x%2B14%29%2F%28x%5E2%2B5x-14%29 ALIGN=MIDDLE  ALT=\"%284x%5E3%2B19x%5E2-61x%2B14%29%2F%28x%5E2%2B5x-14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );