**Correct option (d) none of these**

**Explanation:**

D ≥ 0

(–6m)^{2} –4.1.(9m^{2} –2m + 2) ≥ 0

8m – 8 ≥ 0

m ≥ 1 ........(1)

a.f(3) > 0

1.(32 – 18m + 9m^{2 }– 2m + 2) > 0

9m^{2} – 20m + 11 > 0

9m^{2 } – 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, ∞)