All the values of m for which both roots of the equation x^2 - 2mx + m^2 - 1 = 0 are greater than -2 but less than 4 , lie in the interval: - Mathematics MCQ AIEEE 2006 2026 | ExamTest.live

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All the values of m for which both roots of the equation x^{2} - 2 m x + m^{2} - 1 = 0 are greater than - 2 but less than 4, lie in the interval:

Solution & Step-by-step Explanation

The equation x^{2} - 2 m x + m^{2} - 1 = 0 can be written as: (x - m)^{2} - 1 = 0 ⟹ (x - m)^{2} = 1 x - m = \pm 1 ⟹ x = m + 1, m - 1 The roots are m - 1 and m + 1 .According to the problem: - 2 < m - 1 and m + 1 < 4 From - 2 < m - 1 : m > - 1 From m + 1 < 4 : m < 3 Thus, - 1 < m < 3 .

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All the values of m for which both roots of the equation x^{2} - 2 m x + m^{2} - 1 = 0 are greater than - 2 but less than 4, lie in the interval:

- 2 < m < 0

m > 3

- 1 < m < 3

1 < m < 4

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