Question

Find all zeros of f(x)= x^3-4x^2-5x+20

Answer 1

Possible roots are the factors of 20:  {1, 2, 4, 5, 10, 20} and their negatives.

Use synthetic division.  For example, if I chose 4 as a possible root, the synthetic division setup would be

     ____________
4  /  1   -4   -5   20
            4     0   -20
     _____________
       1    0    -5     0

This tells us that 4 is a root (I was just lucky) and (x-4) is a factor.

The quotient (remaining factor) is (x^2 - 5), which, if factored, yields 

x = sqrt(5) and x = -sqrt(5)


In summary, the roots (or zeros) of   f(x)= x^3-4x^2-5x+20  are
 {sqrt(5), -sqrt(5), 4}