document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964450>Question 964450</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the complex zeros of the polynomial function. <BR>\n" );
document.write( "Write f in factored form. Must show work.\r<BR>\n" );
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document.write( "f(x)=x^4+23x^2+22<BR>\n" );
document.write( "f(x)=<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 #589343 by </B><A HREF=/tutors/aboutme.mpl?userid=t0hierry><B>t0hierry(194)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=t0hierry><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=t0hierry><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=589343\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = (x^2 + 22) (x^2 + 1)\r<BR>\n" );
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document.write( "How did I fid this?\r<BR>\n" );
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document.write( "You know that if f has complex roots, it is the product of simpler functions. Now a polynomial of degree 4 usually has terms in x and x^3. This happens when you multiply four functions. So instead you want to look at the product of two functions in x^2. Let's call them x^2 + a and x^2 + b. You know ab= 22 and a+b=23, this gives you a=22 and b=1 <BR>\n" );
document.write( "whose two complex roots are<BR>\n" );
document.write( "+- i sqrt(22)<BR>\n" );
document.write( "+- i  </SPAN>\n" );
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