JEE Mains · Maths · STD 11 - 1. set theory
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?
- A \(A-B=(-\infty,-3) \cup(5, \infty)\)
- B \(A \cap B=\{-3\}\)
- C \(B-A=(-3,5)\)
- D \(A \cup B=R\)
Answer & Solution
Correct Answer
(A) \(A-B=(-\infty,-3) \cup(5, \infty)\)
Step-by-step Solution
Detailed explanation
\(A: D \geq 0\) \(\Rightarrow \quad(m+1)^{2}-4(m+4) \geq 0\) \(\Rightarrow \quad m^{2}+2 m+1-4 m-16 \geq 0\) \(\Rightarrow \quad m^{2}-2 m-15 \geq 0\) \(\Rightarrow \quad(m-5)(m+3) \geq 0\) \(\Rightarrow \quad m \in(-\infty,-3] \cup[5, \infty)\)…
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