TS EAMCET · Maths · Basic of Mathematics
The common solution set of the inequations \(x^2-4 x \leq 12\) and \(x^2-2 x \geq 15\) taken together is
- A \((5,6)\)
- B \([5,6]\)
- C \([-3,5]\)
- D \((-\infty,-3] \cup[5, \infty)\)
Answer & Solution
Correct Answer
(B) \([5,6]\)
Step-by-step Solution
Detailed explanation
\(\begin{gathered}x^2-4 x \leq 12 \\ \Rightarrow x^2-4 x-12 \leq 0 \Rightarrow(x-6)(x+2) \leq 0\end{gathered}\) \(\Rightarrow x \in[-2,6]\)...(i) Also, \(x^2-2 x \geq 15 \Rightarrow x^2-2 x-15 \geq 0\) \(\Rightarrow(x-5)(x+3) \geq 0\)…
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