document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199782>Question 199782</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello!\r<BR>\n" );
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document.write( "Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions.\r<BR>\n" );
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document.write( "P has degree 2, and zeros 1 + i and 1 - i. \r<BR>\n" );
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document.write( "thanks for the homework help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150159 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=150159\">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( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \alpha\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \beta\"> are roots of the equation <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large ax^2 + bx + c = 0\">, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x - \alpha\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x - \beta\"> are factors of the trinomial <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large ax^2 + bx + c\">.\r<BR>\n" );
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document.write( "So the product of:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x - (1 + i)\right)\left(x - (1 - i)\right)\">\r<BR>\n" );
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document.write( "will result in the desired monic univariate polynomial.\r<BR>\n" );
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document.write( "<b><u>Hints:</u></b>\r<BR>\n" );
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document.write( "1.  Treat <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 1 + i\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 1 - i\"> as single numbers and apply FOIL.\r<BR>\n" );
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document.write( "2.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (1 + i)(1 - i)\"> results in the difference of two squares.\r<BR>\n" );
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document.write( "3.  Remember that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i^2 = -1\">\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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