document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=431282>Question 431282</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the quadratic equation with integral coefficients having the given roots.\r<BR>\n" );
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document.write( "4 + 2i, 4 - 2i\r<BR>\n" );
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document.write( "Thanks!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #299375 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=299375\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The quadratic will have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+%284%2B2i%29+=+x+-+4+-+2i ALIGN=MIDDLE  ALT=\"x+-+%284%2B2i%29+=+x+-+4+-+2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+%284-2i%29+=+x+-+4+%2B+2i ALIGN=MIDDLE  ALT=\"x+-+%284-2i%29+=+x+-+4+%2B+2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > as factors. Hence, the quadratic is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+4+-+2i%29%28x+-+4+%2B+2i%29+=+%28%28x+-+4%29+-+2i%29%28%28x+-+4%29+%2B+2i%29+=+%28x+-+4%29%5E2+-+%282i%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > (applying the difference of two squares)\r<BR>\n" );
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document.write( "Expanding and simplifying, this is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+8x+%2B+16+%2B+4+=+x%5E2+-+8x+%2B+20 ALIGN=MIDDLE  ALT=\"x%5E2+-+8x+%2B+16+%2B+4+=+x%5E2+-+8x+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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