document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=395529>Question 395529</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me rewrite this equation in quadratic form?<BR>\n" );
document.write( "(x-(2+i))(x-(2-i))= 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #280695 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=280695\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We could simply multiply the whole thing out, rewriting as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-2%29-i%29%28%28x-2%29%2Bi%29 ALIGN=MIDDLE  ALT=\"%28%28x-2%29-i%29%28%28x-2%29%2Bi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the other tutor did (so that the difference of two squares can be carried out). This method uses a set of formulas called Vieta's formula:\r<BR>\n" );
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document.write( "The polynomial is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Right off the back we deduce <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+1 ALIGN=MIDDLE  ALT=\"a+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > since we can tell that the x^2 coefficient is 1 without even multiplying. Vieta's formulas say that:\r<BR>\n" );
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document.write( "The sum of the roots of the polynomial is -b/a = -b. Since the roots are 2+i, 2-i, their sum is 4, so b = -4.\r<BR>\n" );
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document.write( "The product of the roots is c/a = c. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Bi%29%282-i%29+=+4+%2B+1+=+5 ALIGN=MIDDLE  ALT=\"%282%2Bi%29%282-i%29+=+4+%2B+1+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (applying difference of two squares) we get c = 5.\r<BR>\n" );
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document.write( "Therefore the polynomial is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+4x+%2B+5 ALIGN=MIDDLE  ALT=\"x%5E2+-+4x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Here are a couple articles on Vieta's formulas, just in case (I rarely see these formulas taught in school, but they're pretty useful to know):<BR>\n" );
document.write( "http://en.wikipedia.org/wiki/Fran%C3%A7ois_Vi%C3%A8te<BR>\n" );
document.write( "http://www.artofproblemsolving.com/Wiki/index.php/Vieta's_Formulas\r<BR>\n" );
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