The value of 'a' so that the equation $x^3 - 6x^2 + 11x + a - 6 = 0$ has exactly three integer solutions is _______.
Step-by-Step Solution
Key Concept: A cubic with integer roots can be factored as a product of linear terms corresponding to each root.
The equation $x^3 - 6x^2 + 11x - 6 = 0$ factors as $(x-1)(x-2)(x-3) = 0$. The roots are $x = 1, 2, 3$ as indicated by the hint. This can be verified by expanding the factored form or by polynomial division.
Correct Answer: 0