document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151677>Question 1151677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Information is given about a polynomial f left parenthesis x right parenthesis whose coefficients are real numbers.  Find the remaining zeros of f.<BR>\n" );
document.write( "Degree​ 4;  ​ zeros: i, -13+1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773501 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=773501\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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;\" >;  ​ => means there is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > zeros\r<BR>\n" );
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document.write( "zeros: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=i ALIGN=MIDDLE  ALT=\"x%5B1%5D=i\"   DISABLED_style= \"max-width:90%; height:auto;\" >, => complex zeros come in pairs, so you also have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=-i ALIGN=MIDDLE  ALT=\"x%5B2%5D=-i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-13+1 ? I guess here are two zeros, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13+ ALIGN=MIDDLE  ALT=\"13+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=13 ALIGN=MIDDLE  ALT=\"x%5B3%5D=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B4%5D=1 ALIGN=MIDDLE  ALT=\"x%5B4%5D=1\"   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=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....plug in given zeros\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-i%29%28x-%28-i%29%29%28x-13%29%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-i%29%28x-%28-i%29%29%28x-13%29%28x-1%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=%28x-i%29%28x%2Bi%29%28x-13%29%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-i%29%28x%2Bi%29%28x-13%29%28x-1%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=%28x%5E2-i%5E2%29%28x-13%29%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2-i%5E2%29%28x-13%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >......since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2=-1 ALIGN=MIDDLE  ALT=\"i%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E2-%28-1%29%29%28x-13%29%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2-%28-1%29%29%28x-13%29%28x-1%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=%28x%5E2%2B1%29%28x-13%29%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2%2B1%29%28x-13%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......multiply all\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E4-14x%5E3+%2B14x%5E2+-14x+%2B+13 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4-14x%5E3+%2B14x%5E2+-14x+%2B+13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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