document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=61715>Question 61715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me please\r<BR>\n" );
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document.write( "Find all three zeros of f(x)=x^3-4X^2+13x+50  given that 3+4i is a zero \r<BR>\n" );
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document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42506 by </B><A HREF=/tutors/aboutme.mpl?userid=jai_kos><B>jai_kos(139)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jai_kos><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=42506\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> F(x)  = x^3 - 4x^2 + 13 x + 50         ---->(1)<BR>\n" );
document.write( "Check the last number, which is 50<BR>\n" );
document.write( "Now find the factors of 50, <BR>\n" );
document.write( "That is 50 ---- 1 , 2 , 5 ,25<BR>\n" );
document.write( "So take all the numbers ---- 1 , -1 ,2 ,-2 ,5,-5,25 , -25<BR>\n" );
document.write( "Now take the first factor 1. put in equation(1), we get<BR>\n" );
document.write( "F(1) = 1^3 - 4*1^2 + 13*1+ 50 = 48<BR>\n" );
document.write( "F(1) is not  equal to zero.<BR>\n" );
document.write( "Like this find for different numbers,<BR>\n" );
document.write( "Then we find that F(-2) is equal to zero.<BR>\n" );
document.write( "So x = -2 is a zero.  ------>(2)<BR>\n" );
document.write( "Now rewrite the above equation we find that...<BR>\n" );
document.write( " x+2 = 0<BR>\n" );
document.write( " Now take this and divide equation (1), <BR>\n" );
document.write( "                   x^2 - 6x + 25<BR>\n" );
document.write( "                 ---------------------------<BR>\n" );
document.write( "(x+2)            | x^3 - 4x^2 + 13 x + 50                       Subtract, we <BR>\n" );
document.write( "get         <BR>\n" );
document.write( "                 | x^3 + 2x^2        <BR>\n" );
document.write( "                 |        - 6x^2 +13x<BR>\n" );
document.write( "                 |        - 6x^2 - 12x                                 Subtract , we get     <BR>\n" );
document.write( "                 |                     25x + 50<BR>\n" );
document.write( "                                       25x + 50                          Subtract,  we get<BR>\n" );
document.write( "                                         0                            \r<BR>\n" );
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document.write( "We  get  x^2 - 6x + 25 <BR>\n" );
document.write( "Simplify this quadratic equation, we get<BR>\n" );
document.write( "x =  - (-6) +-  sqrt(6^2 - 4* 1* 25<BR>\n" );
document.write( "                    2<BR>\n" );
document.write( "x = 3 + 4i  and x = 3 - 4i\r<BR>\n" );
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document.write( "Therefore the zeroes are x = 2 and  x = 3 + 4i , x = 3 - 4i\r<BR>\n" );
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document.write( " </SPAN>\n" );
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