Question

The set of values of ‘a’ for which ax² + (a –2) x – 2 is negative for exactly two integral x, is

• A. (0, 2)
• B. [1, 2)
• C. (1, 2]
• D. (0, 2]

Answer 1

Answer: (B)

[1, 2)

Answer 2

f(x) = ax² + (a – 2) x – 2 = (ax – 2) (x + 1)

f(0) = – 2 & f(– 1) = 0

If a is negative then expression becomes negative for infinite values of x, therefore it must be positive. Expression to be negative for exactly two integral values of x

So $\frac{2}{a}$£ 2 Ž a ³ 1

and $\frac{2}{a}$> 1 Ž a < 2

\ aĪ [1, 2)