Question 1006601
Either use software designed for it or try some other numerical method of your choice (if you know any).  The polynomial given does not have Rational roots.  It does have FOUR REAL roots.  You might try some bounds testing with synthetic division.


Putting y=x^4-4x^3-38x^2-12x+100  into Google.com and clicking GO or ENTER, shows the roots approximately at -3.45, -2.34, 1.42, 8.48.