Question

The values of m(m ∈ R), for which both roots of the equation x²–6mx + 9m² – 2m + 2 = 0 exceed 3 is

(a)  (-∞, 1)

(b)  (-∞, 1)

(c)  (1, ∞)

(d)  none of these

Answer 1

Correct option (d) none of these

Explanation:

D ≥ 0

(–6m)² –4.1.(9m² –2m + 2) ≥ 0

8m – 8 ≥ 0

 m ≥ 1 ........(1)

a.f(3) > 0

1.(32 – 18m + 9m² – 2m + 2) > 0

9m² – 20m + 11 > 0

9m² – 9m – 11m + 11 > 0

9m – 11) (m–1) > 0

m < 1  &  m > 11/9  ...(2)

α + β > 6

6m > 6

From (1), (2) and (3) 

m ∈(11/9, ∞)