JEE Main 2020 (Online) 3rd September Morning ShiftQuestion 1
Consider the two sets : $A=\{m\in\mathbf{R}$ : 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 ?
Sets, Relations and Function
Solution
Real roots: $D=(m+1)^2-4(m+4)=m^2-2m-15\ge0\Rightarrow m\le-3$ or $m\ge5$, so $A=(-\infty,-3]\cup[5,\infty)$. $A\cup B=\mathbf R$ true. $A\cap B=\{-3\}$ true. $A-B=(-\infty,-3)\cup[5,\infty)$ (5 is in $A$, not in $B$), so (C), which omits $5$, is false. $B-A=(-3,5)$ true. Not true: option (C).