Question

The values of m for which exactly one root of x² – 2mx + m² –1= 0 lies in the interval (–2, 4) is

(a)  (–3, –1)∪(3, 5) 

(b)   (–3, –1) 

(c)   (3, 5) 

(d)   none 

Answer 1

Correct option  (a) (–3, –1) ∪ (3, 5)

Explanation

D > 0

ƒ(–2)ƒ(4) < 0

(–2m)² –4.1.(m²–1) > 0

(4 + 4m + m² – 1) (16  – 8m + m² – 1) < 0

4 > 0   (m² +4m + 3) (m² – 8m + 3)

⇒ m ∈  R ......(1)

(m + 1) (m + 3) (m – 3) (m – 5) < 0 

⇒ m ∈(–3, –1) ∪ (3, 5) ......(2)

From (1) and (2) , m ∈ (–3, –1) ∪ (3, 5)