The range of $a$ for which the equation $x^2 + ax - 4 = 0$ has its smaller root in the interval $(-1, 2)$ is

For the smaller root of x^2 + ax - 4 = 0 to be in (-1, 2), let f(x) = x^2 + ax - 4. Since the product of roots is -4, one root is positive and one is negative. The smaller root is the negative one. We need the negative root to be in (-1, 2), which means it must be in (-1, 0). Thus, f(-1) > 0 and f(0) < 0. f(-1) = 1 - a - 4 = -3 - a > 0 => a < -3. f(0) = -4 < 0 (always true).