JEE PYQ: Sets And Relations Question 6
Question 6 - 2020 (03 Sep Shift 1)
Consider the two sets:
$A = {m \in \mathbf{R} : \text{both the roots of } x^2 - (m+1)x + m + 4 = 0 \text{ are real}}$ and $B = [-3, 5)$.
Which of the following is not true?
(1) $A - B = (-\infty, -3) \cup (5, \infty)$
(2) $A \cap B = {-3}$
(3) $B - A = (-3, 5)$
(4) $A \cup B = \mathbf{R}$
Show Answer
Answer: (1)
Solution
$A = {m \in \mathbf{R} : x^2 - (m+1)x + m + 4 = 0 \text{ has real roots}}$
$D \geq 0$
$\Rightarrow (m+1)^2 - 4(m+4) \geq 0$
$\Rightarrow m^2 - 2m - 15 \geq 0$
$A = {(-\infty, -3] \cup [5, \infty)}$
$B = [-3, 5) \Rightarrow A - B = (-\infty, -3) \cup [5, \infty)$
BETA
