document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285095>Question 285095</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider a polynomial equation of z^4 - z^3 - 5z^2 - z - 6 = 0 .<BR>\n" );
document.write( "i. Show that z = -i is a root of the polynomial equation.<BR>\n" );
document.write( "ii. Write its conjugate root.<BR>\n" );
document.write( "iii. Find the other two roots. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #206749 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=206749\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i. -plug in -i for z and see if it works.<BR>\n" );
document.write( "ii-complex roots come in pairs one positive and one negative so i should also work.<BR>\n" );
document.write( "iii-(x-i) and (x+i) are factors so (x^2-1) is a factor<BR>\n" );
document.write( "divide z^4 - z^3 - 5z^2 - z - 6 = 0 by (x^2-1) to find the other factors<BR>\n" );
document.write( "z^2-z-6  factors into (z-3) (z+2) and so the other roots are 3 and -2\r<BR>\n" );
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