document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=957105>Question 957105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Form a polynomial f(x) with real coefficients having the given degree and zeros.<BR>\n" );
document.write( "Degree 4; zeros: 3, multiplicity 2; 4i\r<BR>\n" );
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document.write( "f(x)=a(__________________) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #584818 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=584818\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given:<BR>\n" );
document.write( "Degree <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >; <BR>\n" );
document.write( "zeros: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, multiplicity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4i ALIGN=MIDDLE  ALT=\"4i\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then you also have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4i ALIGN=MIDDLE  ALT=\"-4i\"   DISABLED_style= \"max-width:90%; height:auto;\" > (complex roots always come in pairs)\r<BR>\n" );
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document.write( "use zero product formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28%28x-3%29%5E2%28x-4i%29%28x%2B4i%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28%28x-3%29%5E2%28x-4i%29%28x%2B4i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28%28x%5E2-6x%2B9%29%28x%5E2%2B4i%2Ax-4i%2Ax-16i%5E2%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28%28x%5E2-6x%2B9%29%28x%5E2%2B4i%2Ax-4i%2Ax-16i%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28%28x%5E2-6x%2B9%29%28x%5E2-16%28-1%29%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28%28x%5E2-6x%2B9%29%28x%5E2-16%28-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28%28x%5E2-6x%2B9%29%28x%5E2%2B16%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28%28x%5E2-6x%2B9%29%28x%5E2%2B16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x%5E4-6x%5E3%2B25x%5E2-96x%2B144%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x%5E4-6x%5E3%2B25x%5E2-96x%2B144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );