document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=930626>Question 930626</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation, in standard form, of a polynomial with real coefficients that has roots at 2, 1&#8722;2i, and 1+4i, and passes through the point (0,98). \r<BR>\n" );
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document.write( "Your answer should include only (decimal) numbers, the letter \"x\", and the characters \"+\", \"-\", and \"^\" \r<BR>\n" );
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document.write( "f(x)=___________ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #565186 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=565186\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write the equation, in standard form, of a polynomial with real coefficients that has roots at :\r<BR>\n" );
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document.write( "<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=1-2i ALIGN=MIDDLE  ALT=\"1-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >, complex roots always come in pairs, so you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B2i ALIGN=MIDDLE  ALT=\"1%2B2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > too<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B4i ALIGN=MIDDLE  ALT=\"1%2B4i\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-4i ALIGN=MIDDLE  ALT=\"1-4i\"   DISABLED_style= \"max-width:90%; height:auto;\" > as well\r<BR>\n" );
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document.write( "passes through the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=98 ALIGN=MIDDLE  ALT=\"98\"   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-2%29%28x-%281-2i%29%29%28x-%281%2B2i%29%29%28x-%281%2B4i%29%29%28x-%281-4i%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is coefficient\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%5E5-6x%5E4%2B34x%5E3-96x%5E2%2B173x-170%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x%5E5-6x%5E4%2B34x%5E3-96x%5E2%2B173x-170%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since passes through the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=98 ALIGN=MIDDLE  ALT=\"98\"   DISABLED_style= \"max-width:90%; height:auto;\" >) set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=98 ALIGN=MIDDLE  ALT=\"f%28x%29=98\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   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=98=a%280%5E5-6%2A0%5E4%2B34%2A0%5E3-96%2A0%5E2%2B173%2A0-170%29 ALIGN=MIDDLE  ALT=\"98=a%280%5E5-6%2A0%5E4%2B34%2A0%5E3-96%2A0%5E2%2B173%2A0-170%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=98=a%28-170%29 ALIGN=MIDDLE  ALT=\"98=a%28-170%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=a=98%2F%28-170%29 ALIGN=MIDDLE  ALT=\"a=98%2F%28-170%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=a=-0.5764705882352941 ALIGN=MIDDLE  ALT=\"a=-0.5764705882352941\"   DISABLED_style= \"max-width:90%; height:auto;\" > exact value, and for more accurate result I will use exact value\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-0.5764705882352941%28x%5E5-6x%5E4%2B34x%5E3-96x%5E2%2B173x-170%29 ALIGN=MIDDLE  ALT=\"f%28x%29=-0.5764705882352941%28x%5E5-6x%5E4%2B34x%5E3-96x%5E2%2B173x-170%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=-0.576470588235294x%5E5%2B3.45882352941176x%5E4-19.6x%5E3%2B55.3411764705882x%5E2-99.7294117647059x%2B98 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "we can round it and get shorter form, but zeros will not be exact\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-0.58x%5E5%2B3.46x%5E4-19.6x%5E3%2B55.34x%5E2-99.7x%2B98 ALIGN=MIDDLE  ALT=\"f%28x%29=-0.58x%5E5%2B3.46x%5E4-19.6x%5E3%2B55.34x%5E2-99.7x%2B98\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  \r<BR>\n" );
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document.write( " </SPAN>\n" );
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