<PRE><B>Question 119078</B>
The given equation is: f(x)= {{{x^3- 8x^2 + 25x - 26 }}}


To find the zeros of the given polynomial, we go in for the trail and error method.


when we plug in x = 2 in the above equation we find that it is one of the zeros of the polynomial.

hence the other roots are found by the method of synthetic division.


 2|1   - 8    25  -26
   0     2   -12   26
-----------------------
   1     -6   13   |0 

(x - 2)(x^2 - 6x + 13) 


one root is = 2

and the other 2 roots are found by solving the quadratic equation, using the formula


{{{x = (-(-6))+- sqrt( 36-52 ))/(2) }}} 


{{{x = (6 +- isqrt(16))/(2)}}} 


{{{x = (6 +- 4i)/2 }}}


{{{x = 3 +-2i }}}


thus the other 2 roots.

</PRE>