If a, b are the roots of 2x^2 + 6x + b = 0 and α/β + β/α > 2, then b lies in the interval

Question

If α,β are the roots of 2x² + 6x + b = 0 and α/β + β/α > 2, then b lies in the interval

(A) (0, ∞)

(B)  (−1, ∞)

(C)  (−∞, 0)

(D)  (−∞, 0]

Answer 1

Correct option  (C)  (−∞, 0)

α and β are roots of  2x² + 6x + b = 0 Therefore

α + β = -3 ......(1)

α/β  = b/2      .....(2)

Now,

From Eqs. (1), (2) and (3), we have