Sum of fourth powers of the roots of x³+x+1=0

[zorro]

Homework Statement

The sum of the fourth powers of the roots of the equation x³+x+1=0 is?

The Attempt at a Solution

Is there any shortest method to find out the answer using some formulae? I know a method but its very very lengthy and time consuming.

 

[rock.freak667]

Is it this method you know or another method?

 

[zorro]

I was just looking for that. Thank you so much!