TS EAMCET · Maths · Quadratic Equation
The set of all values of \(x\) which satisfy both the inequations \(x^2-1 \leq 0\) and \(x^2-x-2 \geq 0\) simultaneously is
- A \((-1,2)\)
- B \((-1,1)\)
- C \((-2,-1)\)
- D \(\{-1\}\)
Answer & Solution
Correct Answer
(D) \(\{-1\}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { (d) } \quad x^2-1 \leq 0 \Rightarrow(x+1)(x-1) \leq 0 \\ & \therefore \quad x \in[-1,1\} \\ & x^2-x-2 \geq 0 \Rightarrow(x-2)(x+1) \geq 0 \\ & \therefore \quad x \in(-\infty,-1] \cup[2, \infty) \\ & \therefore \quad x \in\{-1\} .\end{aligned}\)
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