Multiple choice

If $\alpha, \beta$ are the roots of the equation, $x^2 -2mx +m^2- {1} = 0$ then the range of values of $m$ for which $\alpha, \beta \in (-2, 4)$ is:

  1. $(\frac{-1}{2}, \frac{3}{2} )$
  2. $(\frac{1}{2}, \frac{3}{2} )$
  3. $( -\infty , \frac{-1}{2}) \cup ( \frac{3}{2} , \infty )$
  4. $(-1,3)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The roots are x = (2m +/- sqrt(4m^2 - 4(m^2-1))) / 2 = m +/- 1. So roots are m-1 and m+1. For both to be in (-2, 4), we need -2 < m-1 and m+1 < 4. This gives m > -1 and m < 3.

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