TS EAMCET · Maths · Quadratic Equation
The set of all values of \(\mathrm{x}\) for which the inequalities \(\mathrm{x}^2-7 \mathrm{x}+10 \geq 0\) and \(2 \mathrm{x}+3-\mathrm{x}^2>0\) hold simultaneously is
- A \((-\infty, 2]\)
- B \((3, \infty)\)
- C \((-1,2]\)
- D \([2,3)\)
Answer & Solution
Correct Answer
(C) \((-1,2]\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text x^2-7 x+10 \geq 0 \\ & (x-2)(x-5) \geq 0 \\ & \therefore \quad x \in(-\infty, 2] \cup[5, \infty) \\ & \Rightarrow \quad 2 x+3-x^2>0 \\ & \Rightarrow \quad x^2-2 x-3 < 0 \\ & \Rightarrow \quad(x-3)(x+1) < 0 \\ & \Rightarrow \quad x \in(-1,3) \\ &…
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