Q31 / 75 · JEE Main 2020 (03 Sep Shift 1) · Mathematics

Consider the two sets:
$A = {m \in R :$ both the roots of $x^{2} - (m + 1) x + m + 4 = 0$ are real $}$ and $B = [- 3, 5)$
Which of the following is not true?

Solution

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

$\Rightarrow m^{2} - 2 m - 15 \geq 0 \Rightarrow (m - 5) (m + 3) \geq 0$

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

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

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

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

$B - A = (- 3, 5)$

$A \cup B = R$

Hence, the correct answer is option: 'A'.