Explanation

(b)
According to the equation,
$D \geq 0,\ - 2 < - \frac{b}{2a} < 4,\ \ f(4) > 0$ and $f( - 2) > 0$
Now, $D \geq 0;\ \ \ \ \ 4m^{2} - 4m^{2} + 4 \geq 0$
$\Rightarrow \ \ \ \ 4 > 0\ \forall\ m \in R$ ...(i)
$- 2 < - \frac{b}{2a} < 4;\ - 2 < \left( \frac{2m}{2.1} \right) < 4$
$\Rightarrow \ - 2 < m < 4$ ...(ii)
$f(4) > 0$
$\Rightarrow 16 - 8m + m^{2} - 1 > 0\ \Rightarrow (m - 3)(m - 5) > 0$
$\Rightarrow \ - \infty < m < 3$ and $5 < m < \infty$ ...(iii)
And $f( - 2) > 0$
$\Rightarrow \ \ \ 4 + 4m + m^{2} - 1 > 0$
$\Rightarrow \ \ \ (m + 3)(m + 1) > 0$
$\Rightarrow \ - \infty < m < - 3$ and $- 1 < m < \infty$ ...(iv)
$\therefore$ From Eqs. (i), (ii), (iii) and (iv), we get $m$ lie between $- 1$ and 3