document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=677975>Question 677975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial f(x)  of degree 3 with real coefficients and the following zeros.\r<BR>\n" );
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document.write( "-4, -1, i\r<BR>\n" );
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document.write( "Thanks in advance for your help<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 #421124 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=421124\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think you may have meant one of two things. Either the degree is supposed to be 4, or -1 was supposed to be -i.  As you may know, imaginary roots come in conjugate pairs, so with i, we are guaranteed -i to be a root as well. So if -4,-1,i are roots then -i is a root as well, which gives us degree 4.\r<BR>\n" );
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document.write( "So I'll solve it both ways.\r<BR>\n" );
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document.write( "If you meant -4,-1,i  with degree 4, that's\r<BR>\n" );
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document.write( "(x+4)(x+1)(x-i)(x+i)\r<BR>\n" );
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document.write( "[x^2+5x+4][x^2+1] = x^4 + 5x^3 + 5x^2 + 5x + 4\r<BR>\n" );
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document.write( "If you meant -4,-i,i then that's\r<BR>\n" );
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document.write( "(x+4)(x-i)(x+i)\r<BR>\n" );
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document.write( "(x+4)(x^2+1) = x^3 + 4x^2+ x + 4 </SPAN>\n" );
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