document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1000165>Question 1000165</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Form a polynomial f(x) with real coefficients having the given degree and zeros.\r<BR>\n" );
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document.write( "Degree 4; zeros: -2-5i; -4 multiplicity 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617661 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=617661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x+4)^2 deals with root of -4 with multiplicity 2.<BR>\n" );
document.write( "(1/2a)(-b+/- sqrt(b^2-4ac) has to be -2 +5i and -2 -5i, because complex roots are conjugates.  The square root has to be -25 or some multiple of it. b^2-4ac=-25*constant.   b=2 or some multiple of it. Let's make a 1, (1/2)(4+/- sqrt(16-4c)). Here, b is 4. To get 5i, I need the square root of 100, because I want 10i, which divided by 2 gives 5i.  So 4c=116, and c=29.<BR>\n" );
document.write( "x^2-4x+29 would be that polynomial.<BR>\n" );
document.write( "(x+4)^2(x^-4x+29)<BR>\n" );
document.write( "x^4+4x^3+13x^2+168x+464\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-50%2C1000%2Cx%5E4%2B4x%5E3%2B13x%5E2%2B168x%2B464%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-50%2C1000%2Cx%5E4%2B4x%5E3%2B13x%5E2%2B168x%2B464%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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