$p(x) = x^{3} - 2x^{2} + ax - b $
Lets roots = a, b, c.
sum of roots = (a+ b+ c) = 2.
$ ab + bc + ca = a \\
abc = b \\
a^{3} + b^{3} + c^{3} = (a + b + c)^{3} + 3abc - (a + b + c)(ab +bc +ca) \\
=> 0 = 2^{3} + 3b - 2a \\
=> 2a = 8 + 3b. \\
= > a = 4 + 3b/2 $
C = (a,b) = ( 1, -2) , ( 4, 0) , ( 7, 2) .... infinite possibile set (a,b).
So, Ans should be - A.