document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=731291>Question 731291</A>: <I><SPAN STYLE=\"word-break: break-all;\"> one zero of f(x)=x^4-3x^3-12x-16 is -2i. what are the other zeros of the function?\r<BR>\n" );
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document.write( "I have NO clue how to solve this I think my calculator is needed which is a TI-83 PLUS but clarification if needed on how to solve this problem! Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #447080 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=447080\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> TWO of the roots are -2i and +2i.  The -2i was given.  The +2i is a root because complex roots to polynomial equations occur in conjugate pairs.\r<BR>\n" );
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document.write( "Using those two roots, find the corresponding quadratic factors of f(x), and use polynomial division to find the other quadratic factor.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2i%29%28x-2i%29=x%5E2-%282i%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B2i%29%28x-2i%29=x%5E2-%282i%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=x^2-(-1)*4=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5E2%2B4%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5E2%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You want to divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-3x%5E3-12x-16 ALIGN=MIDDLE  ALT=\"x%5E4-3x%5E3-12x-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4 ALIGN=MIDDLE  ALT=\"x%5E2%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You should use the divisor in the form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B0%2Ax%2B4 ALIGN=MIDDLE  ALT=\"x%5E2%2B0%2Ax%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The polynomial division, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E4-3x%5E3%2B0%2Ax%5E2-12x-16%29%2F%28x%5E2%2B0%2Ax%2B4%29=x%5E2-3x-4 ALIGN=MIDDLE  ALT=\"%28x%5E4-3x%5E3%2B0%2Ax%5E2-12x-16%29%2F%28x%5E2%2B0%2Ax%2B4%29=x%5E2-3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and that quadratic polynomial is factorable into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x-4%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So the function is factorable into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f%28x%29=%28x%5E2%2B4%29%28x%2B1%29%28x-4%29%29 ALIGN=MIDDLE  ALT=\"highlight%28f%28x%29=%28x%5E2%2B4%29%28x%2B1%29%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The roots found which were not given in the description  but were asked for are -1 and +4. </SPAN>\n" );
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