Multiple choice

If both the roots of the equation x2 - 2mx + m2 - 1 = 0 are greater than - 2 but less than 4, then

  1. -1 < m < 3

  2. 1 < m < 4

  3. -2 < m < 0

  4. 1 < m < 3
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A Correct answer
Explanation

For the roots of x^2 - 2mx + m^2 - 1 = 0 to lie between -2 and 4, we analyze the roots x = m +/- 1. Thus, the roots are m-1 and m+1. We require -2 < m-1 and m+1 < 4. This simplifies to -1 < m and m < 3.

AI explanation

Factoring the equation x2 - 2mx + m2 - 1 = 0 as a perfect square minus one yields (x - m)2 - 1 = 0, which further factors into (x - m - 1)(x - m + 1) = 0. This gives the roots as x = m + 1 and x = m - 1. Applying the condition that both roots must be greater than -2 and less than 4 means -2 < m - 1 and m + 1 < 4, which results in -1 < m < 3.

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