If equation ${x^2} + ax + a + 1 = 0$ has integral roots then sum of possible integral values of 'a' is

Let the integer roots of the equation be r and 1, since their difference r - 1 must equal a to ensure an integer value. The product of the roots gives the equation r = a + 1, which means the possible values for the roots are (2, 1) and (-1, 1) yielding a = 1 and a = -2. The sum of these possible integral values of a is 1 + (-2) = 0.

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