document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=986181>Question 986181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three roots of a fourth-degree polynomial equation with rational coefficients are 5+&#8730;3, –17, and 2-&#8730;4. Which number also is a root of the equation?<BR>\n" );
document.write( "A. 17<BR>\n" );
document.write( "B. 2+&#8730;4<BR>\n" );
document.write( "C. 4-&#8730;2<BR>\n" );
document.write( "D. 5-&#8730;3<BR>\n" );
document.write( "How does this make sense? I thought that if you switched the addition/subtraction symbol, then you will have the other root. So shouldn't A, B, and D all be correct?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #606984 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=606984\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29=2 ALIGN=MIDDLE  ALT=\"sqrt%284%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-sqrt%284%29=2-2+=+0 ALIGN=MIDDLE  ALT=\"2-sqrt%284%29=2-2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. They made this root a bit more complicated than it had to be to confuse you. The three roots, as simple as they can get, are given as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Bsqrt%283%29 ALIGN=MIDDLE  ALT=\"5%2Bsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-17 ALIGN=MIDDLE  ALT=\"-17\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Rule: if you have a polynomial with rational coefficients, and you have a root <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Asqrt%28c%29 ALIGN=MIDDLE  ALT=\"a%2Bb%2Asqrt%28c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b%2Asqrt%28c%29 ALIGN=MIDDLE  ALT=\"a-b%2Asqrt%28c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > must also be a root as well.\r<BR>\n" );
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document.write( "So if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Bsqrt%283%29 ALIGN=MIDDLE  ALT=\"5%2Bsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a root, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-sqrt%283%29 ALIGN=MIDDLE  ALT=\"5-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > must also be a root (note: a = 5, b = 1, c = 3 in this case)\r<BR>\n" );
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document.write( "Final Answer: <font color=\"red\">Choice D)</font> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-sqrt%283%29 ALIGN=MIDDLE  ALT=\"5-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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