document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=665655>Question 665655</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Form a polynomial f(x) with real coefficients having the given degree and zeros.  Degree: 4; zeros: 2i and -5i<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #413989 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=413989\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Complex roots occur in pairs, ie + or - 2i and + or - 5i.<BR>\n" );
document.write( "Your four (for 4th order polynomial) factors are<BR>\n" );
document.write( "(1) f(x) = (x+2i)(x-2i)(x+5i)(x-5i) which multiplies (FOIL) to<BR>\n" );
document.write( "(2) f(x) = (x^2+4)*(x^2+25) or<BR>\n" );
document.write( "(3) f(x) = x^4 + 29x^2 + 100<BR>\n" );
document.write( "Note the real coefficients result from the use of complex pairs.<BR>\n" );
document.write( "Also note that (2i)*(-2i) = -4(i)^2, but i^2 = -1, so (2i)*(-2i) = +4. </SPAN>\n" );
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