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asked ago in Mathematics by (66.6k points)
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The values of m for which both roots of the equation x– mx + 1 = 0 are less than unity is

(a) (-∞, -2)

(b) (-∞, -2)

(c) (-2, -∞)

(d)  none of these

1 Answer

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answered ago by (59.2k points)
selected ago by
 
Best answer

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]

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