document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=694244>Question 694244</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been trying to figure this out for days and I am stuck! The question is: Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 5-i,square root of 17 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #427808 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=427808\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You need to also have as zeros the conjugates of those numbers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Bi ALIGN=MIDDLE  ALT=\"5%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%2817%29 ALIGN=MIDDLE  ALT=\"-sqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "That way, when you multiply factors involving conjugates, the irrational/imaginary parts cancel out.<BR>\n" );
document.write( "Your polynomial must be of grade 4, and the one with a leading coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be calculated as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-sqrt%2817%29%29%28x%2Bsqrt%2817%29%29%29%28%28x-%285-i%29%29%28x-%285%2Bi%29%29%29=%28x%5E2-17%29%28%28x-5%2Bi%29%28x-5-i%29%29=%28x%5E2-17%29%28%28x-5%29%5E2-i%5E2%29=%28x%5E2-17%29%28x%5E2-10x%2B26%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "I left the last multiplication for you to do. </SPAN>\n" );
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