Consider the two sets: A = m ∈ R: both the roots of x ^ 2 - ( m + 1...

Since both roots are real ${\left(m + 1\right)}^{2} - 4\left(m + 4\right) \ge 0$

$⇒ {m}^{2} - 2m - 15 \ge 0 ⇒ \left(m - 5\right)\left(m + 3\right) \ge 0$

$⇒ m \in ( - \infty , - 3 ] \cup [ 5, \infty )$

$⇒ A = ( - \infty , - 3 ] \cup [ 5, \infty )$

$A - B = \left(- \infty , - 3\right) \cup [ 5, \infty )$

$A \cap B = \left\{- 3\right\}$

$B - A = \left(- 3, 5\right)$

$A \cup B = R$