The correct options are
A a,b,c can be any negative integers
B a,b,c can be any positive rational numbers
As both the roots are negative, so
α+β<0⇒−ba<0⇒ba>0⋯(1)α×β>0⇒ca>0⋯(2)
When a>0, using equation (1) and (2), we get
b>0, c>0
Similarly, when a<0, using equation (1) and (2), we get
b<0, c<0
Hence, a,b,c has to be of same sign.