document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=621340>Question 621340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given a quadratic equation with rational coefficients with a root of 5-i:                                                      a)What is another root to the equation?                                                                                                      b) What are the factors of the equation?                                                                                                      c) What is the quadratic equation with the given root? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390687 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=390687\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given a quadratic equation with rational coefficients with a root of 5-i: <BR>\n" );
document.write( "a)What is another root to the equation? <BR>\n" );
document.write( "complex conjugate of 5-i is the other root:<BR>\n" );
document.write( "5+i<BR>\n" );
document.write( "b) What are the factors of the equation? <BR>\n" );
document.write( "s1 = 5-i<BR>\n" );
document.write( "s2 = 5+i<BR>\n" );
document.write( "(x - (5-i)) and (x - (5+i))<BR>\n" );
document.write( "(x-5+i) and (x-5-i)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "c) What is the quadratic equation with the given root?<BR>\n" );
document.write( "b/a = -(s1+s2)<BR>\n" );
document.write( "b/a = -(5-i+5+i)<BR>\n" );
document.write( "b/a = -(5+5)<BR>\n" );
document.write( "b/a = -10<BR>\n" );
document.write( ".<BR>\n" );
document.write( "c/a = s1s2<BR>\n" );
document.write( "c/a = (5-i)(5+i)<BR>\n" );
document.write( "c/a = 25-i^2<BR>\n" );
document.write( "c/a = 25-(-1)<BR>\n" );
document.write( "c/a = 25+1<BR>\n" );
document.write( "c/a = 26<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x^2 + (-10)x + 26<BR>\n" );
document.write( "x^2-10x+26\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );