Question
Question: The values of m for which exactly one root of equation x<sup>2</sup> –2mx + m<sup>2</sup> – 1 = 0 li...
The values of m for which exactly one root of equation x2 –2mx + m2 – 1 = 0 lies in the interval (–2, 4) is
A
(–,)
B
(–3, –1)
C
(3, 5)
D
(–3, –1) Č (3, 5)
Answer
(–3, –1) Č (3, 5)
Explanation
Solution
f(–2) . f(4) < 0
(4 + 4m + m2 – 1) (16 – 8m + m2 – 1) < 0
Ž (m + 3) (m + 1) (m – 3) (m – 5) < 0
Ž m Ī (–3, – 1) Č (3, 5)