Describe the number and type of roots for the polynomial (how many real and complex?). x 3 + 5x 2 – 4x – 2 = 0

1 x ^3 + 5x^ 2 – 4x – 2 = 0

Note.....if we can add the coefficietnts and get 0, then 1 is a root........

So......1 + 5  - 4 - 2  = 0   ...so 1 is a root....

Performiing some syntthetic division to find the remaining polynomial, we have......

1  [ 1    5     - 4      -2  ]

            1      6        2   

      _____________

       1    6      2      0

The remaining polynomial  is    x^2 + 6x  + 2.......

The other two roots can be found by using the quadratic formula....they are  

-3 - sqrt(7)   and  -3 + sqrt (7) 

All these roots are real