document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112257>Question 112257</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/013227650x/algebrahomeworkh>Precalculus Graphical Numerical Algebraic</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> given that 1+3i is a zero of f(x)= x^4-2x^3+5x^2+10x-50 find all zeros and write a linear factorization </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #81932 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=81932\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if 1+3i is a zero (root) then (x-1-3i) is a factor\r<BR>\n" );
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document.write( "since complex roots occur in conjugate pairs, (x-1+3i) is also a factor\r<BR>\n" );
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document.write( "so (x-1-3i)(x-1+3i) or x^2-2x+10 is a factor\r<BR>\n" );
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document.write( "(x^4-2x^3+5x^2+10x-50)/(x^2-2x+10)=x^2-5\r<BR>\n" );
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document.write( "this gives (x+sqrt(5)) and (x-sqrt(5)) as the two other factors </SPAN>\n" );
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