document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=7732>Question 7732</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The degree three polynomial f(x) with real coefficients and leading<BR>\n" );
document.write( "coefficient 1, has 4 and 3 + i among its roots. Express f(x) as a<BR>\n" );
document.write( "product of linear and quadratic polynomials with real coefficients. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4492 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=4492\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">   4 and 3 + i among its roots\r<BR>\n" );
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document.write( " Another complex root must be the conjugate of 3+i, ie 3-i.<BR>\n" );
document.write( " The corresponding quadratic monic equation is x^2  -6 x + 10 = 0 (why?)<BR>\n" );
document.write( " [Hint: in one step sum and product of 3+i & 3-i]<BR>\n" );
document.write( " Hence, f(x) = (x-4)(x^2  -6 x + 10)\r<BR>\n" );
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document.write( " Kenny </SPAN>\n" );
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