Possible roots to try using synthetic division are -10,-5,-2,-1,1,2,5,10.
-1 | 1 -3 5 -1 -10
|
| -1 4 -9 10
|___________________________________
1 -4 9 -10 0
2 | 1 -4 9 -10
|
| 2 -4 10
|__________________________________
1 -2 5 0
Both -1 and +2 are roots for the degree four expression. The factorization of the equation would be
and you would like to find any other REAL roots, because that is what your
question specifies.
The discriminant of the found quadratic factor is , negative, therefore has NO REAL ROOT.
The solution for the original given equation is therefore .