The rational root theorem tells you all roots are of the form
±(factor of 2)/(factor of 3)
We know one of the roots is -1 and all roots are negative, so the remaining roots must be of the form
-(factor of 2)/(factor of 3)
which is to say, two of
-1/3, -2/3, -1, -2
Since the roots are distinct, they must be -2 and -1/3. Then the factorization of the given polynomial is
(x +1)(x +2)(3x +1)
which multiplies out to be
3x³ +10x² +9x +2
a = 10
b = 9