Given the roots are in A.P. so let a-d, a, a+d be the roots
From equation, sum of roots = 1
Sum of two roots taken at a time = +b
Product of two roots = -c
∴ (a-d)+ (a)+ (a+d) = 1
=) 3a = 1
=) a =
Also, (a-d)a+ a(a+d)+ (a-d)(a+d) = b
=) a^{2} – ad + a^{2} + ad + a^{2} – d^{2} = b
=) 3a^{2} – d^{2} = b
=) 3x – d^{2} = b
=) d^{2} = b -
Now, since d is a real number,
Also,
(a-d)(a)(a+d) = -c
=) a(a^{2} – d^{2}) = -c
=)
=)
=)
=)
Again,
∴ Only option (c) b= -1 , c =1 could be true .
Correct Answer: 9