document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190967>Question 190967</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is an update of a previous problem which I copied wrong <BR>\n" );
document.write( "I need to find a polynomial of degree 4 with integer coefficients that have roots:-2,5,and 3+2i such that P(3)=-80. I know to use the conjugate of 3+2i which is 3-2i, and I know how to put them in the f(x)=a(x-r1)(x-r2...format, but from there I get tripped up and can't figure out what to do with P(3)=-80. Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143377 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=143377\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is an update of a previous problem which I copied wrong <BR>\n" );
document.write( "I need to find a polynomial of degree 4 with integer coefficients that have roots:-2,5,and 3+2i such that P(3)=-80. I know to use the conjugate of 3+2i which is 3-2i, and I know how to put them in the f(x)=a(x-r1)(x-r2...format, but from there I get tripped up and can't figure out what to do with P(3)=-80. <BR>\n" );
document.write( "-------------------------------------------<BR>\n" );
document.write( "P(x) = a(x+2)(x-5)(x-(3+2i))(x-(3-2i))<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Use P(3) = -80 to determine the value of \"a\":<BR>\n" );
document.write( "----<BR>\n" );
document.write( "P(3) = a(5)(-2)(-2i)(2i) = -80<BR>\n" );
document.write( "a(-10)(4) = -80<BR>\n" );
document.write( "a(-40) = -40<BR>\n" );
document.write( "a = 2<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Now you know the equation is:P(x) = 2(x+2)(x-5)(x-(3+2i))(x-(3-2i))<BR>\n" );
document.write( "====================================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );