document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1099067>Question 1099067</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial with integer coefficients that satisfies the given conditions.<BR>\n" );
document.write( "Q has degree 3 and zeros &#8722;4 and 1 + i\r<BR>\n" );
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document.write( "I do not know how to do this could you please help me.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713466 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=713466\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the other zero is 1-i,since they are conjugate.<BR>\n" );
document.write( "one factor is (x+4)<BR>\n" );
document.write( "Using the quadratic formula, one wants to end up with  [2+/- sqrt (-4)]/2, because that will reduce to 1+/-i\r<BR>\n" );
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document.write( "Therefore, using the quadratic formula, b=-2 and (b^2-4ac) must be -4, because the square root of -4 is +/-2i, and 2i/2=1, assuming a=1, which is the easiest case for Ax^2+Bx+C<BR>\n" );
document.write( "That would be 4-4ac=-4 and a=1<BR>\n" );
document.write( "so 4-4c=-4<BR>\n" );
document.write( "-4c=-8<BR>\n" );
document.write( "c=2<BR>\n" );
document.write( "the quadratic factor is x^2-2x+2<BR>\n" );
document.write( "The polynomial is the product of the two factors<BR>\n" );
document.write( "x^3+4x^2-2x^2-8x+2x+8<BR>\n" );
document.write( "x^3+2x^2-6x+8<BR>\n" );
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