document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=415954>Question 415954</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you find the complex zeros of f(x)=x^3-8x^2+25x-26? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #291553 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=291553\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)=x^3-8x^2+25x-26\r<BR>\n" );
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document.write( "The best way to find all the roots of functions higher than second degree is to start by displaying this function on a graphing calculator to see if there are any real roots.  As you can see from the graph below,the given cubic function has only one real root=2.  <BR>\n" );
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document.write( "Next, divide the function by (x+2),by long division or use synthetic division:\r<BR>\n" );
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document.write( "When you do this, you will get a quotient=x^2-6x+13<BR>\n" );
document.write( "Solving this second degree equation using the quadratic formula:<BR>\n" );
document.write( "a=1, b=-6, c=13\r<BR>\n" );
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document.write( "x=-(-6)+-sqrt((-6)^2-4*1*13)/2*1<BR>\n" );
document.write( " =(6+-sqrt(36-52)/2<BR>\n" );
document.write( " =(6+-sqrt(-16))/2<BR>\n" );
document.write( " =(6+-4i)/2<BR>\n" );
document.write( " =3+-2i\r<BR>\n" );
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document.write( "Ans:<BR>\n" );
document.write( "one real root, 2<BR>\n" );
document.write( "two complex roots,3+2i and 3-2i<BR>\n" );
document.write( "See the graph below:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-5%2C+5%2C+-50%2C+50%2C+x%5E3-8x%5E2%2B25x-26%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-5%2C+5%2C+-50%2C+50%2C+x%5E3-8x%5E2%2B25x-26%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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