document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193367>Question 193367</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1602773033/algebrahomeworkh>saxon algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Write the simplest polynomial function with zeros 7+i and square root 5. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145200 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=145200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The answer to that question really depends on what you think (or more to the point what your instructor thinks) is simpler, a 3rd degree polynomial function with irrational coefficients or a 4th degree polynomial function with integer coefficients.\r<BR>\n" );
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document.write( "Perform the indicated multiplications\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x - \sqrt{5}\right)\left(x - (7 + i)\right)\left(x - (7 - i)\right)\">\r<BR>\n" );
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document.write( "to obtain the 3rd degree polynomial.  You should end up with irrational coefficients on the constant, 1st, and 2nd degree terms.\r<BR>\n" );
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document.write( "Perform the indicated multiplications\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x - \sqrt{5}\right)\left(x + \sqrt{5}\right)\left(x - (7 + i)\right)\left(x - (7 - i)\right)\">\r<BR>\n" );
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document.write( "to obtain the 4th degree polynomial with integer coefficients.\r<BR>\n" );
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document.write( "<b>Update:</b>\r<BR>\n" );
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document.write( "It just occurred to me that you could multiply:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x - \sqrt{5}\right)\left(x - (7 + i)\right)\">\r<BR>\n" );
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document.write( "to obtain a 2nd degree polynomial with complex coefficients.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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