The correct option is: (C) -1, -6
Explanation:
x4 + x3 + 8x2 + ax + b is exactly divisible by x2 + 1
=> Remainder must be zero.
(a - 1)x + (b - 7) = 0
=> a - 1 = 0 and b - 7 = 0 => a = 1 and b = 7
Now, ax2 + bx + 6 becomes x2 + 7x + 6.
x2 + 7x + 6 = x2 + 6x + x + 6 = 0
= x(x + 6)+1(x + 6) = 0
= (x + 1)(x + 6) = 0 => x = -1,-6