The minimum value of ƒ(x) = x^2 + 2bx + 2c^2 is greatest than the maximum value of g(x)= –x^2 – 2cx + b^2 ,

Question

The values of m for which both roots of the equation x² – mx + 1 = 0 are less than unity is

(a) (-∞, -2)

(b) (-∞, -2)

(c) (-2, -∞)

(d)  none of these

Answer 1

Correct option   (b)  (–∞,–2]

Explanation:

D ≥ 0

(–m)² – 4.1.1  ≥ 0

(m – 2) (m + 2)  ≥  0

⇒ m ∈ (–∞,–2] ∪ [2,∞) .... (1)

a. f(1) > 0

1.(1 – m + 1) > 0

m < 2

m ∈(–∞,–2]  ...(2)

α + β < 2

m < 2

m ∈(–∞,–2]  ...(3)

Form (1), (2) and (3) we have

m ∈(–∞,–2]