document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=26803>Question 26803</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find a third-degree polynomial equation with rational coefficients that has the roots -5 and 4+i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #14602 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=14602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find a third-degree polynomial equation with rational coefficients that has the roots -5 and 4+i<BR>\n" );
document.write( "IF THE COEFFICIENTS OF POLYNOMIAL ARE REAL ,THEN COMPLEX ROOTS CAN OCCUR ONLY IN CONJUGATES.SO IF 4+I IS A ROOT THEN 4-I IS ALSO A ROOT.SO,WE HAVE ALL THE 3 ROOTS FOR THE 3 RD. DEGREE POLYNOMIAL...HENCE THE POLYNOMIAL IS GIVEN BY...<BR>\n" );
document.write( "(X+5)(X-(4+I))((X-(4-I))=0<BR>\n" );
document.write( "(X+5){(X-4)^2-I^2}=0<BR>\n" );
document.write( "(X+5)(X^2+16-8X+1)=0<BR>\n" );
document.write( "=(X+5)(X^2-8X+17)=0<BR>\n" );
document.write( "=X^3-8X^2+17X+5X^2-40X+85=0<BR>\n" );
document.write( "=X^3-3X^2-23X+85=0 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );