Question

Let S be the set of values of a for which 2 lies between the roots of quadratic equation x² + (a + 2)x - (a + 3)x = 0. Then S is given by

(A)  (−∞, −5)

(B)  (5, ∞)

(C)  (−∞, −5]

(D)  [5, ∞)

Answer 1

Correct option (A)  (- ∞,-5)

See Fig. 

x² + (a + 2)x - (a + 3) = 0

As f(2) < 0, we have

⇒ 4 + 2(a + 2) - (a + 3) < 0

⇒ a + 5 < 0

⇒ a < − 5

⇒ a ∈(-∞, -5)